Lesson video

Hello, my name is Dr.

Ronson and this lesson is packed with useful information.

I hope it helps you in your life too.

Let's get started then.

Welcome to today's lesson from the unit of Maths and the Environment.

This lesson is called Making a Journey and by the end of today's lesson we will be able to assess the implications of making a journey in different ways.

The lesson will introduce a new keyword, which is commute.

A commute is a regular journey made between a person's home and their place of work.

The lesson will also use these previous keywords as well.

Feel free to pause the video if you want to remind yourself what they mean and press play when you're ready to continue.

The lesson is broken into three learning cycles and we're going to start by calculating journey times for different methods of transport.

Here we have a table that shows census data taken from the Office of National Statistics, that's the ONS.

The data is about the distances that people commuted in the year 2021.

For example, the top row of data shows us that there were 3,057,913 people that travelled less than two kilometres to the place of work.

Now this data could be easier to interpret if it was represented visually.

For example, we could represent it something like this, a bar chart.

This bar chart shows the same information about how far people commuted in the year 2021.

So over to you to do something with this bar chart now.

Which is the modal group according to this data? Pause the video while you write down and answer and press play when you're ready to see what it is.

The modal group is the group that has the greatest frequency, which is this one here, two kilometres to less than five kilometres.

Approximately how many people travel between 10 kilometres and 20 kilometres? And give your answer to one significant figure.

Pause while you do that and press play for an answer.

Well, we're looking at this bar here, the fourth one down and what we can see is the bar is pretty close to three million people.

So to one significant figure it would be approximately three million.

True or false then? Over 9 million people travel less than 10 kilometres to work.

Is this true or false? And justify your answer.

Pause the video while you write something down and press play for an answer.

Well this is true and even though we don't know the exact number of people who travel each those distances or exactly how far they travel of that matter, what we can see is that there are over three million people in each of those first three groups.

And if you add up each of those three millions, and bear in mind that each 'em is more than three million, what you get is that the whole group that is under 10 kilometres has a frequency of over 9 million.

Here we have another table now that shows the average speeds for three methods of transport when travelling through urban areas.

By urban areas it means towns and cities and so on.

So when you're driving, you'll be stopping quite a lot for traffic lights and turning left and right and so on.

When walking, you gotta be across the road and things like that.

So it kinda slows you down a little bit.

And from the table we can see that on average people walk five kilometres per hour in urban settings, they cycle 20 kilometres per hour and drive 35 kilometres per hour.

Now a person lives 1.

5 kilometres from their place of work.

Let's calculate their expected journey time using each method of transport.

We could work this out using this formula here.

Speed equals distance divided by time, but we could rearrange this formula to make timeless subject because time is what we are working out.

So when it comes to walking, we know that they're going 1.

5 kilometres at an average speed of five kilometres per hour.

So we do 1.

5 divided by 5 and that'll give us 0.

3 hours.

And if we want to convert hours into minutes, we can do that by multiplying our answer by 60 and that would give us 18 minutes.

For cycling, we could do 1.

5, the distance divided by 20 the speed, and that would give us 0.

075 hours.

We can convert it to minutes and that would give us 4.

5 minutes.

And for driving we could do 1.

5 divided by 35 and that would give us 0.

042 and there are more decimals.

Before we round it, let's convert it to minutes.

We times by 60 and once we round it to the nearest minutes, we get three minutes.

So let's check what we've learned.

A person lives four kilometres from the place of work, using information at the table, how much time could they expect to spend travelling if they cycle to work? And give your answer in hours.

Pause while you work out and press play for an answer.

We can do 4 divided by 20 to get 0.

2 hours.

So if it takes 0.

2 hours to cycle to work, how long is this in minutes? Pause while you write down answer and press play when you're ready to see what it is.

You can convert it to minutes by multiplying by 60 and that'll give you 12 minutes.

So how about if they drive to work instead, how much time could they expect to spend travelling if they drive? And give your answer this time to the nearest minutes.

Pause while you work it out and press play for an answer.

Well, you can first work it out in hours by doing 4 divided by 35 and then multiply your answer by 60 to convert to minutes and should get seven minutes to the nearest minutes.

Okay, and so two for task A.

This task contains one question and here it is.

The table shows distances of three commutes and it tells you the average speeds via three different methods of transport.

Could you please fill in the blanks and table to calculate the estimated journey times for each journey using each method of transport? Then the last question at the bottom there is more of an opinion question.

Based on information you work out, which method of transport would you choose for each length of journey? There's no right or wrong answer to that.

It's really more of what what you think and how you feel based on the information.

But try and justify your answer as much as you can.

Pause the video, why work through this and press play when you are ready to look at some answers.

Okay, let's take a look at some answers.

For the two kilometre journey, it would take 24 minutes to walk, 6 minutes to cycle, and 3 minutes to drive.

For the eight kilometre journey, it will take 96 minutes to walk, 24 minutes to cycle and 40 minutes to drive.

And for the 16 kilometre journey, it would take 192 minutes to walk.

That is well over three hours and it'll take 48 minutes to cycle or 27 minutes to drive.

That's just under half an hour.

And then you have to say which method of transport you would choose for each length for journey? Now there's no right or wrong answer here and answers will differ depending on your personal preferences, but hopefully, you've justified your answers in some sort of way.

For example, Laura says, "I would prefer to always use the fastest mode of transport." Maybe she's in a bit of a rush.

So she would drive no matter what.

Jacob, however likes walking.

So if he could, he would walk no matter what the length of journey is.

However, walking for over an hour could be impractical when it comes to commuting.

Imagine walking three hours to get to work and then going to work and then walking three hours to get home again.

It'd just take a lot of time in your day.

So in those cases he said I'll cycle for longer journeys.

And then here we have Aisha who says, "I'd like to spend a little bit of time commuting but not too long.

An ideal amount of time for me would be between 15 and 30 minutes." Based on what Aisha said here, she would walk for if it was two kilometres.

She would cycle, if it was eight kilometres and she would drive if it was 16 kilometres.

Well done so far.

Now we've looked at how long journeys take using different methods of transport.

Let's look at how much carbon emissions is produced when using different methods of motorised transport.

When petrol or diesel vehicles make a journey they consume fuel.

What factors may affect the amount of fuel that is consumed during a journey? Perhaps pause the video while you think about some examples yourself and then press play when you're ready to continue together.

There are lots of different factors that may affect the amount of fuel that is consumed.

Well, let's take a look at a few examples.

One could be the length of the journey.

The longer the journey is, the more fuel the vehicle will need.

Another could be whether driving in a town or city or on a motorway.

Cars can be more efficient when they are driving on a motorway than they are in a town or city because in a town or city they are stop and starting quite regularly.

The another thing could be the size of the vehicle itself.

Heavier vehicles may consume more fuel, they can move or the size of the engine for that matter or even the type of fuel can affect how much fuel is consumed.

Now some vehicles do use fuel more efficiently than others and the fuel efficiency of a vehicle is often expressed in terms of miles per gallon.

This is the average number of miles that a vehicle can travel using one gallon of fuel.

Now there are different types of gallons that are different sizes depending on country.

For example, the gallon which is used in the UK is an imperial gallon and this is a different size to the gallon that is used in the USA.

During this lesson, wherever we say gallon, we are referring to a UK imperial gallon.

Anyway, fuel efficiency can differ depending on the cars.

For example, a small car may travel 50 miles per gallon on average, but a larger car may travel only 35 miles per gallon on average.

The fuel that we use during a journey produces CO2 emissions.

We can estimate the amount of CO2 emissions per mile using the formula we can now see on the screen.

On the left we have, what we are working out that is the emissions per mile, which is measured in grammes.

On the right we have a division.

The numerator is the amount of CO2 produced per gallon of fuel and that is measured in grammes.

And the denominator has the fuel efficiency of the vehicle which is measured in miles per gallon.

For example, the average CO2 emissions for a petrol car is nine kilogrammes per gallon.

The average fuel efficiency of a small car is 50 miles per gallon.

How much CO2 emissions does it produce per mile? Well, here's our formula, but before we substitute any numbers in, let's check if we have all the correct units.

What we can see here is we have nine kilogrammes, but in our formula that measure is in grammes.

So before we substitute any numbers in, it's worth converting any measurements we have.

So they are in the same units as our formula.

Nine kilogrammes is equal to 9,000 grammes.

So we can work this out by doing 9,000 divided by 50, which would give 180.

And that means the car producers 180 grammes of CO2 emissions per mile.

So let's take this example a little bit further.

A person's car produces 180 grammes of CO2 emissions per mile.

They live nine miles from their place of work.

How much emissions does the car produce during a single journey to work? This problem could be modelled using a ratio table that looks something a bit like this.

The top row shows us the distance that has travelled and the bottom row shows us the amount of CO2 emissions.

And in that middle column we have the information from the top line that one mile of distance produces 180 grammes of CO2 emissions.

And what we want to do is work out how much CO2 emissions is produced by nine miles of journey? There's a couple different ways we can work this out.

We could use multipliers going horizontally, but which means we are times in one mile by nine to get nine miles.

So we do 180 multiply by 9 or we can consider the multipliers to get us from the top row to the bottom row, which is 180.

Either way, we're gonna be multiplying together 9 and 180 and that will give us 1,620 grammes, which is 1.

62 kilogrammes of CO2 emissions for each journey.

So let's extend this problem further.

The person doesn't just drive to work, they drive home from work as well.

So that means they make two car journeys per day.

Each journey produces 1.

62 kilogrammes of CO2 emissions and the person works 225 days per year.

So how much CO2 emissions does the car produce in a year travelling to and from work? Well, we could word this out by doing 1.

62, which is the amount per journey times it by two because it's two journeys per day and times it by 225 because it's 225 days and that would give us 729 kilogrammes.

So the car produces around 729 kilogrammes of CO2 emissions per year by commuting.

So let's check what we've learned with a similar scenario and you'll work out some things yourself now.

The average CO2 emissions for a petrol car is nine kilogrammes per gallon and the average fuel efficiency of a large car is 35 miles per gallon.

You're given a foreman to work with.

How much CO2 emissions does this car produce per mile and give your answer accurate to three significant figures.

Pause while you work it out and press play for an answer.

Well, you're going to divide 9,000 by 35.

9,000 because 9 kilogrammes is 9,000 grammes and that would give 257 grammes of CO2 emissions per mile given to three significant figures.

So let's take this problem further now.

They live 13 miles from their place of work.

How much emissions does the car produce in a single journey to work a one way journey? Give your answer in kilogrammes.

Pause while you write it down and press play for an answer.

When you multiply 13 by 257, you get your answer in grammes, which then you can divide by 1,000 to get 3.

341 kilogrammes of CO2 emissions for each journey.

Now the person makes two car journeys per day travelling to work and travelling home from work.

Each journey produces 3.

341 kilogrammes of CO2 emissions and the person works for 192 per days per year.

Could you please work out the amount of CO2 emissions that the car producers in a whole year by travelling to and from work? Pause while you work it out and press play for an answer.

If you multiply the amount of missions per journey by the number of journeys per day by the number of days per year and then round your answer to three significant figures, you would get 1,280 kilogrammes of CO2 emissions per year by commuting.

Okay, so to you then for task B, this task contains two questions and here is question one.

Pause while you do it and press play for question two.

Here is question two.

Pause while you do this and press play to look at some answers.

Okay, let's go through some answers.

For question one, there are plenty of different ways you can work this out, but here is one way you could break the problem down.

You could start by working out the amount of emissions per mile and that'll be by dividing 9,000 grammes by 45 and that would give you 200 grammes of CO2 emissions per mile.

And then once you know that you can work out the amount of emissions per journey, the journey is six miles, so we can do 200 times 6 and that give us 1,200 grammes of CO2 emissions per journey or 1.

2 kilogrammes.

Once you know that you can work out the amount of emissions per day, a person makes two journeys per day.

So you could do 1.

2 if you're working in kilogrammes, multiply by 2 to get 2.

4 kilogrammes of CO2 per day and then you can work out the amount of emissions per year by multiplying by 223 and that would give 535.

2 kilogrammes of CO2 emissions per year.

That's approximately 535 kilogrammes when rounded to three significant figures.

Another way that we can break the problem down is like this, we could work out the number of miles a person travels per day by doing six miles per journey multiplied by two 'cause there's two journeys per day and that gives 12 miles in total for every day.

And then we could work out the number of miles a person travels each year by multiplying that by 223 and that gives 2,676 miles per year.

We could work out the emissions per mile in the same way we did in the previous method by dividing 9,000 by 45 to give 200 grammes of CO2 per mile and then we can multiply that by the number of miles per year and that would give us 535,200 grammes, which is approximately 535 kilogrammes of CO2 per year once it's rounded to three significant figures.

In question two you have a similar scenario, but this time it's involving people travelling by bus.

40 people live six miles from their place of work and travel on the same bus.

Now in reality, these 40 people aren't all gonna get on the bus at the same time and get off the bus at the same time.

Some will get on before and after each other and there will be other people on the bus who travel further and so on.

But for the sake of this problem, let's simplify it to just simply the facts we have here, 40 people travelling six miles on the same bus.

Let's now use information to work out the amount of CO2 emissions produce per passenger per year by commuting on bus.

Once again, there are different ways you can work out, but here's one way you can break the problem down.

We can work out the amount of emissions per mile by the bus.

That'll be about dividing the 10,000 by 8, which means the bus will produce 1,250 grammes of CO2 per mile or 1.

25 kilogrammes.

Then we can work out the amount of emissions per journey by more multiply by six.

That'll give 7.

5 kilogrammes of CO2 per journey.

And then we can multiply that by two 'cause each of these people are making two journeys a day.

So that's 15 kilogrammes of CO2 per day.

And then across the year that would be 3,345 kilogrammes of CO2 per year.

Now that's a lot more emissions than what we saw in question one with a single person travelling by car.

But we need to remember there are 40 people on this bus.

So let's divide that 3,345 between those 40 people, which means per person it works out as 83.

6 kilogrammes of CO2 per year per person when round to three significant figures.

Now you can also without in using alternative methods and hopefully get the same answer.

Great work so far.

Let's now assess the implications of making a journey in one more way by calculating the cost of the journey.

Let's start with a reminder of this fact here that the fuel economy of a vehicle is often expressed in terms of miles per gallon and that means the average number of miles that the vehicle can be expected to travel using one gallon of fuel.

Now there is a problem with using miles per gallon when it comes to the UK and that is in the UK petrol diesel is sold in litres.

So we have two different units of volume at play here, but we can use the fact that one gallon is approximately 4.

546 litres to convert between these units.

That means we can convert from gallons to litres by multiplying by 4.

546 or we can convert from litres to gallons by dividing by 4.

546.

So now we've got that fact, let's look an example together.

A person drives nine miles to work.

The average fuel efficiency of their car is 50 miles per gallon.

Petrol costs 142.

9 pence per litre.

And we have a reminder of the conversion between gallons and litres.

What is the total cost of petrol for the journey? Now this is quite a complex problem.

Perhaps pause video while you think about what steps might take along the way to find our solution? And then press play when you are ready to work through it together.

Now like I said, this is quite a complex problem.

So let's start by making a plan before we do any calculations.

We could start by calculating the amount of petrol used and do that in gallons because we are given 50 miles per gallon to work with.

And then we can convert that into litres because the cost is given to us per litre.

And then we could calculate the cost of the petrol once we have those figures.

Let's start with step one.

Let's calculate the amount of petrol used in gallons.

We know the vehicle travels 50 miles per gallon and the person drives nine miles to work.

We could model this problem using a ratio table that looks something a bit like this.

We have the miles in the top row and the amount of gallons used in the bottom row and we can see that they travel 50 miles per one gallon of petrol.

So if we want to work out how much petrol used in nine miles, the easiest way in this case would probably to be to to divide the numbers in the top row by 50 to get the numbers in the bottom row.

Nine divided by 50 is 0.

18.

So that means each journey uses 0.

18 gallons of petrol.

So now we've got that, let's convert that amount into litres because the cost of petrol is given in litres.

We know each journey uses 0.

18 gallons of petrol and we've got the conversion that one gallon is approximately 4.

546 litres.

So we can multiply 0.

18 by 4.

546 and that will give us that number there, which suggests each journey uses 0.

81828 litres of petrol.

Now you might be tempted to round that number at this point, but don't forget we've got more to do with this problem and if we round our answer here, it means we'll lose accuracy in the future.

So let's leave this number unrounded for as long as we can so we can maintain accuracy until we get our final answer.

The final step is to calculate the cost of the petrol.

So each journey uses that amount of petrol.

The cost of petrol is 142.

9 pence per litre.

So if we multiply those two numbers together, we get this cost which is expressed in pence.

Now to convert to pounds, we only want to divide by a hundred and then we're going to want to round to nearest penny.

And if we do that, we'll get one at 117 pence, which is 1 pound 17 pence.

So it means the cost of petrol for each journey is that amount there, 1 pound 17 pence.

Let's extend this problem further now.

We know that each journey, either to work or home from work costs 1 pound 17 pence in terms of the amount of petrol used on the journey.

The person makes two journeys per day when commuting, one journey going to work and the other journey going home from work.

And they do this on 225 days of the year.

What is the annual cost of petrol for this person to commute to work by driving? Well, it can work out by multiplying the cost per journey by the number of journeys per day by the number of days in the year.

And that will give us 526.

5, which when we express it in terms of money, it means commuting by car costs approximately 526 pounds and 50 pence per year for petrol.

Let's now extend the problem even further.

We know how much a person spends on petrol to commute to work, but they also pay for some other things as well in order to use their car to commute.

For example, they pay 80 pound per month for car insurance and the annual cost of maintenance for the car is 650 pounds.

So let's assume that they only use their car so that they can drive to work just to simplify the problem ever so slightly.

I know they might use the car for all things, but let's just keep it at that.

How much do they spend in total on their car per year? Well, we can word that out by adding the amount of money you spend per year on petrol by 12 lots of the amount of money they spend on car insurance per month and then also add the annual cost of the maintenance.

And that will give us 2136.

5, which means when we express it in terms of money, it means the person spends approximately 2136.

50 on the car per year so that he could commute to work.

So let's check what we've learned and the scenario for you to work with.

A person drives 12 miles to work, they travel to and from work on 225 days of the year.

And the average fuel efficiency of the car is 40 miles per gallon.

You're told that petrol costs 138.

9 pence per litre and you're also reminded of what the conversion is between gallons and litres.

On the left hand side you can see a series of calculations that reaches a solution.

And on the right hand side you can see suggestions for what each calculation may represent, but they're jumbled up.

Could you please match each calculation with what it represents in the context? So for example, write down either A, B, C, D, or E for the top line of working and then the same for the second line and so on.

Pause the video while you do that and press play when you're ready to see answers.

Let's take a look at this together.

The top line which says 1 divided by 40 works out the gallons of petrol consumed per mile.

That's because you know the car travels 40 miles with one gallon.

So if you wanna work out as one mile, you can divide your one gallon by 40 and that would give 0.

025.

That means the next line of working works out the amount of gallons of petrol consumed per journey because there are 12 miles in the journey.

And then the next line of working would be a conversion from gallons per journey to litres per journey.

That's the multiply by 4.

546.

That's our conversion between gallons and litres.

So if the 1.

3638 is the litres of petrol consumed per journey, when that is multiplied by the 1.

389, well that's working out the cost per journey where the 1.

389 is the cost of petrol per litre in pounds.

And then the bottom line of working would be the cost per year.

We multiplied it by two 'cause there are two journeys per day and multiplied it by 225 'cause our 225 days where a person travels to work in a year.

That means the total cost would be 852 pounds and 44 pence per year for petrol.

Here is the exact same problem again, but this time, the solution has been calculated using a different series of steps.

Could you please match each line of working with what it represents in context this time? Pause while you do that and press play when you're ready for answers.

Let's take a look at this together.

The top line says 12 times 2 times 225.

Well 12 is the number of miles in the journey.

2 is the number of journeys per day and 225 the number of days when a person travels in the year.

So that means the 5,400 is the number of miles travelled per year in total.

The 1 divided by 40 we've seen that before.

That is the gallons of petrol consumed per mile.

And then that has been multiplied by the number of miles travelled per year, which means that third line of working is the gallons of petrol that is consumed per year.

The next line has taken the 135 and more applied it by that familiar 4.

546.

That looks like a conversion from gallons into litres.

So it's the amount of petrol used per year expressed in litres.

And then we can see that 1.

389, that is the cost per litre.

So that means that last line of working is the annual cost of petrol, but this time is expressed in pence.

Okay, so to you for task C, this task contains one question.

And here it is, pause while you do it and press play for answers.

Okay, let's go through some answers.

In this question, you're given some information about person's commute to work in their vehicle.

In part A, you have to work out how much they spend on petrol per year commuting by car? Well, there are lots of different ways you can work this out, but here is one example of a solution strategy.

You could start by work out the miles per year by multiplying six miles per journey by two journeys per day by 225 days per year.

That means a person drives 2,700 miles per year commuting to and from work.

You could also work out how much petrol the car consumes for every mile it drives.

And if you do this in gallons, you would do 1 divided by 45, which gives 0.

02 recurring gallons of petrol per mile.

And we're not going to round that 0.

02 recurring because we haven't got our final solution yet.

Once we know that and we know how many miles per year, we can work out the amount of gallons per year by multiplying those together.

And it says 60 gallons is consumed per year by this car driving to and from work.

We can convert that to litres by multiplying by 4.

546 to get 272.

76 litres per year.

And then we can multiply that by the cost of petrol per litre and we get the total cost be 406 pounds and 14 pence per year for the petrol for commuting.

So you've worked that out for part A and we're going to use that again shortly.

In part B, you had to take into account the other costs involved in running a car.

The car insurance is 65 pounds per month and the annual maintenance costs sum to 820 pounds.

And now assume that the car is only used for commuting, how much they spend in total? You could do the amount for petrol plus 12, lots of the amount per month for insurance, plus the amount for maintenance in the year, and that will give 2006 pounds and 14 pence per year on the car for commuting.

And part C, the person's considering selling the car and commuting buy bus because they're selling the car, they no longer need to pay the insurance or the maintenance costs or pay for petrol and so on.

The weekly bus pass in their town is 22 pounds per week.

Now assume that they would buy a weekly bus pass for every week of the year.

It'll probably a few weeks because they'll have some times when they're on holiday and not working and so, but let's assume that they would buy a pass for every single week of the year.

Would commute and buy bus cost more or less money per year than commute and buy car? You need to justify your answer.

Well, there are 52 weeks in a year, so the annual cost of buying a weekly bus pass will be 22 multiplied by 52, which is 1,144 pounds.

So yes, that would cost less than the amount of money spent on the car, which is 2006.

14 pounds.

Fantastic work today.

Now let's summarise what we've learned.

There may be many options for how we choose to travel to a place, and there are various factors that may affect which method of transport is preferable.

Examples include how long it would take travelling by each mode of transport or the cost involved with each choice or the environmental impact of each method of transport, particularly with a motorised method.

Calculations can be used to make comparisons between different methods of transport to support our decision making.

And making the same journey multiple times means the impact of our journey is multiplied.

So the impact might be so much for one journey, but if you met that journey twice a day for 225 days a year, that impact is multiplied by quite a lot.

Well done today.

Have a great day.