Lesson video

Hello, my name is Dr.

Rowlandson and we have a great lesson store today.

So, let's get started.

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

This lesson is called Considering a Route and by the end of today's lesson, we will be able to plan a journey and consider which available form of transport is best.

The lesson will make use of a previous keyword, which is estimate.

A quick estimate for a calculation is obtained from using approximate values, often rounded to one significant figure.

The lesson is broken into two learning cycles.

In the first part, lesson will going to be planning journeys that can be made directly.

For example, a journey that involves just one bus or just one train.

Then, the second part lesson, we're going to be planning journeys that require some kind of changeover.

For example, you may take two buses, or two trains, or a bus, and then a train and so on.

Let's start off though with planning a direct journey.

When we plan a journey, there are often sometimes multiple options available for the method of transport.

For example, we could travel by car, or by bus, or by train, or by underground train, and there are many of options available as well.

What factors may affect which mode of transport somebody chooses for their journey? Perhaps pause the video while you think of some examples of this and press play when you're ready to continue together.

Well, there are many factors that may affect a person's choice or transport, so let's just take a look at a few examples together.

Examples could include the time a journey would take using each mode of transport.

For example, how long would the journey take in the car compared to how long it would take on the bus.

It could also involve the cost of a journey using each mode of transport or the availability of different forms of transport in their area.

For example, they may live near a train station or there may be a train station near to where they're trying to go to.

There may not be.

The availability of car parking spaces.

If you're planning to drive somewhere, you need to know what you can park somewhere in the facility of where you're trying to get to or why you need to take that into account when it comes to how long it would take.

How much road traffic there may be at that particular time of travel.

You may be stuck in traffic jams if you drive, which you won't be if you are on the train.

Also, how busy public transport may be at different times of travel as well.

Also, the environmental impact of each mode of transport may also be considered too.

Let's consider some of these factors together now.

Journey planners, such as apps or websites, can be helpful when planning a journey.

They can estimate how long a journey could take using different modes of transport and they can suggest possible routes which you might take, which trains or buses you might catch, and so on.

While these provide suggested routes, you always remember the final decision about a journey is made by the person who is travelling.

Also, not all of those factors we discussed in that previous slide may be considered by a journey planning app or website page.

Therefore, decisions about mode of transport may depend on factors that are not considered by a journey planner.

Let's take a look at an example together.

Izzy and her father are planning to visit a museum.

They're trying to decide whether it'll be quicker to travel by car or by bus.

Now, we'll look at the precise details of the journey shortly.

Let's start by just considering generally why might one mode of transport take longer than the other.

So for example, why might travelling by bus take more time than travelling by car.

Perhaps pause video and think about what factors may affect how long a bus journey may take and why it could take longer than travelling by a car and press play when you're ready to continue together.

There may be many reasons for this, but let's take a look at a few examples together.

Izzy and her father will need to walk to a bus stop.

So, one thing that could affect how long it would take is how far they live from the nearest bus stop that would take 'em in the right direction.

The bus may take an indirect route rather than travel by the fastest route.

It may travel around some housing estates, for example, around different towns, so that could take longer for that reason too.

Buses stop regularly to pick up people and drop off people along the way as well.

So, those stops will take time as well.

However, a bus journey is not always longer than a car journey, so why might travelling by bus take less time than travelling by car? Pause video while you think about some reasons for this and press play when you're ready to continue together.

Once again, there may be many reasons for this, but let's take a look at a couple examples together.

A bus may be able to overtake busy traffic by using a bus lane.

Sometimes, you have very busy roads where the cars are queuing and are all stationary, but there'll be a bus lane, so a bus will be able to overtake all those cars and be quicker.

Another reason might be that there's not a car park near the museum.

For example, Izzy and her father may drive the park in a car park, but that car park is about a 30 minutes walk from the museum.

That means it'll take more time for that reason.

And there are plenty of other reasons as well for each of these two questions.

Now, we've talked about cars and buses, but another option could be to travel by train.

Why might travelling by train take less time than travelling by bus? Pause the video and think about this and press play when you're ready to continue together.

Let's take a look at a few examples.

Trains tend to travel faster than buses.

Also, trains are not affected by road traffic.

Yes, there are sometimes bus lanes that help the bus, but not always.

Trains have fewer stops compared to a bus journey of the same length.

So, why might travelling by train take more time than travelling by bus? Pause video and think about this and press play when you're ready to continue together.

Let's take a look at a couple examples of this.

There are fewer railway stations in bus stops.

For example, in a city, there may be hundreds of bus stops, but just one train station, so you may have to walk further to get to or from a railway station than you do a bus stop.

Another reason is that trains on a route might be less frequent than buses.

A train might be only every half an hour, while a bus may be every 15 minutes.

So, those two things should be taken into consideration when it comes to planning how long a journey would take.

That's our example.

Izzy and her father are planning to visit a museum.

They consider how much time it would take to travel by bus.

The nearest bus stop to their home is a 10-minute walk away.

They would board the bus at 13:42 and now alight the bus at 14:13.

Those times are in 24 hour clock and they're the same as 1:42 PM and 2:13 PM The nearest bus stop to the museum is a five-minute walk away.

So with all that taken into account, what would be the total journey time? Well, let's take a look at this.

First, let's work out how long that bus journey would take.

They would board the bus at 13:42 and a light at 14:13.

Well, one way to calculate this could be to break it into two parts.

Consider how many minutes there are between 13:42 and 14:00 hours, and that would be 18 minutes.

And then, consider how many minutes there are between 14:00 hours and 14:13, and that would be 13 minutes.

So altogether, there would be 31 minutes spent on the bus.

And then the amount of time spent walking would be a sum of 10 and five, so that'd be 15 minutes.

So, altogether the total journey time will be the sum of 31 minutes, which is spent on the bus, and 15 minutes, which is spend walking, and that'll be 46 minutes altogether.

So, let's check what we've learned.

Izzy and her father are planning to visit the museum.

They consider how much time it would take to travel by car.

There is some information on the screen to help you.

Could you please work out the total journey time Pause video while you do it and press play for an answer.

The answer is 45 minutes.

You would spend 20 minutes walking altogether and 25 minutes driving in the car.

They now consider how much time it would take to travel by train.

Here are some information to help you about their journey.

Could you please calculate their total journey time.

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

The answer is 39 minutes.

You'll spend nine minutes on the train and the four plus five comes from doing the four minutes that takes you from 13:56 to the next hour, which would be 14:00 hours.

And the five is how many minutes to then between 14:00 hours and when they get off a train, which is 14:05.

So altogether, they spend nine minutes on a train.

They spend 20 minutes walking to the train station and 10 minutes walking away from the train station.

So, that's 30 minutes.

So altogether, it'll be 39 minutes.

So now we've considered how much time this journey would take using each mode of transport, let's consider the cost involved.

Izzy and her father consider how much a journey would cost to travel by car.

Let's start by considering how much it would cost in terms of petrol.

A journey planner says that the car park is 6.

8 miles from their home, so they need to drive 6.

8 miles and that would use petrol.

On average, their car travels 40 miles per gallon of petrol.

At the nearest petrol station, it is sold for 142.

9 pence per litre.

Now because the car travels 40 miles per gallon and petrol is sold in litres, we have a gallon to litres conversion to help us along the way.

So using this information, what would be the cost of petrol required for this journey? Let's work through this together.

Well, we could start by using this fact here.

That the car travels 40 miles per gallon of petrol and I can use that fact to work out how much petrol the car is likely to use in a one-mile of the journey.

If the car can travel 40 miles with one gallon of petrol, we could split that one gallon between those 40 miles to work out how much petrol is used in each mile.

One divided by 40 is 0.

025 gallons.

So if the car is likely to use 0.

025 gallons for one mile of a journey, we could multiply it by 6.

8 to work out how much petrol it would use in a 6.

8 mile journey and that would be 0.

17 gallons.

And because we are buying this petrol in litres, we can convert this amount into litres by multiplying by 4.

546.

That means on this journey, the car is likely to use 0.

77282 litres of petrol altogether.

Now, you might be thinking that number has a lot of digits in it.

Why don't we round it? Well, that's because we're going to do some more calculations with it and if you round it too soon, our answer will become inaccurate, because we need to work out how much this amount of petrol will cost.

The cost is 142.

9 pence per litre.

So if you multiply the amount of petrol in litres by the cost per litre, we would get 110.

435 pence, which rounds the pounds and pence as one pound and 10 pence.

So, the cost of the petrol for this journey will be one pound 10.

So, the petrol for one leg of this journey will be one pound 10.

We also need to consider parking as well.

Sometimes, car parks cost money.

Parking in the car park in this case would cost seven pound 40.

And also, you would need to drive home again as well the same distance.

So approximately, the same cost in terms of petrol.

So altogether, what would be the total cost of travelling by car? Well, it would be one pound 10, multiply by two because there are two parts of this journey, driving there and driving back, plus the cost of the car park.

Altogether that would be 9 pound 60.

Now we considered how much it would cost by car, let's consider how much it would cost by bus.

An adult bus ticket costs three pound each way, and a children's bus ticket costs one pound 50 each way.

What would be the total cost of one adult and one child travelling there and back by bus? Well, here's one way you could work it out.

You could work out the total cost of the bus tickets for one leg of the journey.

That'd be doing three pound plus one pound 50 should be four pound 50, and then multiply it by two because there are two parts of this journey, going there and going back.

Altogether, it'd be nine pounds.

Or you could think of it in a different way.

You could work out how much the adult tickets would cost altogether by doing three multiplied by two, and how much the children tickets would cost altogether by doing one pound 50 multiply by two, then adding those together.

The calculations are equivalent.

So, let's check what we've learned.

A car travels an average of 50 miles per gallon.

How many gallons of petrol would it use per mile? Pause video away, work it out, and press play for an answer.

The answer is 0.

02 gallons, which you get from doing one divided by 50.

So, how many gallons of petrol would it use in 15 miles? Pause while you work it out and press play for an answer.

We can take our previous answer and multiply it by 15 to get 0.

3 gallons.

Here's conversion from gallons and litres.

How many litres is equal to 0.

3 gallons? Pause video while you work it out and press play for an answer.

We can multiply 0.

3 by 4.

546, and that would tell us it would be 1.

3638 litres.

A petrol station charges 151.

9 pence per litre.

for petrol.

A one-way journey requires 1.

3638 litres of petrol.

What is the cost of the petrol required for this journey? Pause video while you work it out and press play for an answer.

Here's our answers.

Approximately two pound and seven pence.

A car park charges six pound 20.

So, what would be the total cost of a two-way journey with parking? Pause video while you work it out and press play for an answer.

Two pound seven is the cost of petrol for one way journey.

So, we need to multiply it by two to get both ways and add the cost of the parking.

Altogether, it'd be 10 pounds 34.

Okay, it's all to you for Task A.

This task contains three questions and here is question 1.

You are given a scenario about Jacob and his mother planning a trip to the theatre in a city centre.

You are given some information answering questions to consider.

Pause the video while you do this and press play for question 2.

And here is question 2.

It takes the same scenario, but provides you with information about different options and asks you some questions about those.

Pause video while you do this and press play for question 3.

And here is question 3.

This time it's over to you to plan a journey.

Use a journey planning website or app to plan a journey.

The journey should be from your home to a destination that you could travel to directly by public transport.

For example, you can get there using one bus or one train.

Plan how you'd make this journey by car and by public transport.

And then, compare the time and cost implications of each.

And there are some things you may want to consider along the way at the bottom.

There's no right or wrong answer to this.

It'll be completely dependent on your own context and your own choice, but do show all the things you considered, along with the calculations that support your decision.

Pause video while you do this and press play.

Start looking at some answers.

Okay, let's go through some answers.

In question 1, you had this scenario about Jacob and his mother planning to travel to a theatre in a city centre.

You're told what time they want to arrive.

That's 2:45 PM.

And you're told that they're considering travelling by bus.

So, what's the latest time that they can leave their home to travel by bus? That would be 1:43 PM And what would be the total cost of the journey there and back? It would be six pounds 40.

And then in question 2, we have the same scenario, but this time they're considering travelling by car.

They still want to arrive at the theatre by 2:45 PM.

So based on information you're given, the latest time they can leave the home is 1:55 PM And then when it comes to considering the cost, we should factor in the amount of petrol used and also the amount of money spent for parking.

We could break this calculation down into small steps.

We can work out how many gallons of petrol is used in one mile based on what this car can travel.

That is 45 miles per gallon.

The car would use 0.

02 recurring gallons of petrol per mile.

And then when we consider the journey there and the journey back, the car would travel 18 miles altogether.

So, 18 miles of petrol would be 0.

4 gallons of petrol.

And if we convert that into litres, it would be 1.

8184 litres.

So, the cost of petrol altogether will be 2.

71.

Now if you worked out the amount of petrol used for a nine-mile journey, you would need to multiply that cost by two to account for driving the and back.

But in this case, we've already accounted for the journey there and journey back by multiplying the number of miles by two.

So, we've worked out the cost for 80 miles of journey.

That is 2.

71.

So, all we do now to work out the total cost is add on the cost of parking, which should be eight pound 21.

Then in question 3, you had to plan your own journey by either bus, train, or underground or any other public transport and compare it to the travelling by car, considering the cost, and the time, and implications, showing all your calculations along the way.

Well, your answers this will vary depending on what choices you've made, but hopefully you've laid it out very clearly showing how much each thing would cost along the way and how long each thing would take along the way as well.

You're doing great.

Let's now move on to next part of this lesson where we're going to plan a journey that requires a changeover.

The diagram here illustrates a direct journey that can be made using a single vehicle.

For example, a bus can get you from your starting point to your destination.

However, not all journeys on public transport can be made directly using a single vehicle.

Sometimes, you may need to use multiple vehicles in a single journey.

For example, there might not be a bus that gets you from your starting point directly to your destination.

You may need to first get a bus to another location and then once you're there, get a bus to where you want to go to, or this might be with two trains, or it might be you get a bus first to a train station and then once you're at the train station, you get a train to where you want to go to.

A stage of a journey where we change between buses or trains is sometimes referred to as a connection or a changeover.

A journey that requires a changeover means that additional considerations need to be made when we plan the journey.

We need to consider the amount of time between alighting from one vehicle and boarding the next vehicle, and this is sometimes referred to as a changeover time or a connection time.

For example, the diagram on the screen here illustrates a case where someone gets two trains, the first train takes 30 minutes.

And then once they get to that train station, there's a 15 minute wait until the second train sets off.

And that second train takes 45 minutes.

Altogether, the time would be the sum of 30, 15, and 45, which gives 90 minutes or one hour and 30 minutes.

Now, it may be preferable to have a short change over time.

For example, in this case, the changeover is just four minutes.

So, the total journey time will be shorter.

It'll be 79 minutes or one hour 19 minutes in this case.

But can you imagine what problem might be when a short change over time? When the change over time is short, it increases the risk of missing the connection.

Let's take, for example, Alex here.

Alex's first train arrives five minutes late and that causes him to miss the second train.

That means he has to wait another 29 minutes at the train station.

So altogether, his first train took 35 minutes 'cause it was delayed, so it took a bit five minutes longer.

The change over time was increased to 29 minutes because he missed one train, had to wait a long time for the next train to come.

And then, he had the 45 minutes expected for the second train.

Altogether, that'd be 109 minutes, which would be one hour 49 minutes.

So, you may think a short connection is a good thing for making journeys quicker, but they can also make journeys longer if they have a good chance of missing your second train.

Let's check what we've learned.

Here we have Aisha wants to travel from Town A to Town C.

She plans to catch the 16:55 bus from Town A to Town B.

The bus stop in Town B is a four-minute walk from the train station, and then she plans to catch a train from Town B to Town C.

There's some information about bus times and train times.

What I want you to work out is will she arrive in Town B with enough time to catch the 17:41 train.

And please explain your answer as well.

Pause while you do this and press play for the answer.

The answer is yes, she has enough time.

There is seven minutes for her to make a connection and four of 'em will be spent walking.

So, she has approximately three minutes to spare.

The 16:55 bus arrives in Town B though five minutes late, so what time will she arrive in Town C? Pause while you it work out and press play for an answer.

Even though the bus would arrive before the train sets off, she still needs to walk to the train station, so she would miss the 17:41 train, unless that train is also running late.

Let's assume that train's running on time.

It would mean that she catches the 18:00 train instead and arrives in Town C at 18:50.

Okay, it's over to you for Task B now.

This task contains two questions and here is question 1.

You have a scenario where Sofia has a university interview at an office in London.

She needs to arrive at the office before 11:00 AM.

You're provided with some information about her journey and some questions to answer based on that information.

Pause video while you work this out and press play when you're ready for question 2.

And here is question 2.

It is over to you again to plan your own journey.

This time, you should plan an indirect journey.

The journey should be from your home to a destination that you could travel to by public transport.

However, you would need to make at least one changeover.

In other words, it can't be something you can get to directly by one bus or one train or so on.

You need to change it somewhere.

Plan how you can make this journey by public transport and you may wish to consider the points on the screen there to help you.

Pause video while you do this and press play when you're ready to look at some answers.

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

In question 1, you had the scenario about Sofia trying to get to London for a university interview and she wants to get there before 11:00 AM.

What is the latest possible time that Sofia could leave her home and arrive for the interview? The latest possible time could be 7:53.

In this case, she would leave home at 7:53.

She would catch the 8:03 train from Oakington and that would get her in time to catch the 8:40 train from Elmsville.

And then, she'd have enough time to get to the office for 10:59, but ooh, that's cutting it close.

So, what could go wrong if Sofia leaves at the time you stated in part A the latest possible time? Well, there are lots of different answers you can write here, but here's one example.

The train from Elmsville to London could be delayed, which means she would be late for her interview.

So in part c, you have to suggest a more cautious time that Sofia could leave her home.

There's no definite right or wrong answer here.

It's mostly down to how you might plan this journey based on this information, ensuring that she gets her on time.

An example could be she leaves her home at 7:33, which means she catches the 7:33 train from Oakington, which gets her on time to catch the 8:00 train from Elmsville.

And then, she would arrive at the office at 10:35.

However, the problem with this plan it will only give Sofia three minutes to change trains at Elmsville.

What happens if the Oakington train is delayed or Elmsville could be quite a large train station, which would mean it could be a long walk from the platform where she gets off the train from Oakington to the platform where she gets on the train to London.

So, three minutes might not be enough there.

Another example could be to leave home at 6:53.

She could catch a train at 7:03 from Oakington and that would get her to Elmsville on time to catch the 7:40 train or if she misses that, she's still got the 8:00 train if she, and that will get her own time to London as well.

And if she gets the first train she wanted, the 7:41, it means she can arrive at the office a good hour early and that way she can get herself settled, get herself calm, have a drink, have a bit of food, and get herself ready for her interview.

Good luck, Sofia.

Then question 2, you have to plan your own journey.

Your answer will vary depending on your choices, but hopefully you've explained very carefully where each amount of time comes from on your journey.

Fantastic work today.

Now, let's summarise what we've learned.

There may be many options for how to travel to a place.

Journey planners can aid when deciding how to travel to a location.

However, they do have their limitations.

Various factors can affect which mode of transport is most favourable, such as journey time, cost, environmental impact, and so on.

So, it is important to consider the implications of each form of transport.

Well done today.

Have a great day.