Lesson video

Hi there.

My name is Ms. Lambell.

You've made a superb choice deciding to join me today to do some maths.

Let's get cracking.

Welcome to today's lesson.

The title of today's lesson is Compound Measures for Speed, and that is within the unit Compound Measures.

By the end of this lesson, you will be able to use compound measures for speed.

Two key words, which we'll be referring to a lot during today's lesson are speed and pace.

Speed is the rate at which something is moving.

It is measured as a distance travelled per unit of time.

Pace is a rate of movement.

It is measured as the time taken per unit of distance.

Today's lesson is split into three separate learning cycles.

In the first one, we will look at calculating speed.

Then, we'll move on to looking at problems with speed, and then in the final cycle we will look at pace.

Let's get going with that first one.

We're gonna concentrate firstly, like I said, on calculating speed.

If a car is travelling at a constant speed of 40 MPH, what other facts do we know? Sofia says, "In two hours you would travel 80 miles." Andeep says, "How do you know that?" Sofia's response is, "Well, mph means miles per hour.

So, 40 mph means you travel 40 miles in one hour.

If you drive for twice the length of time, you will travel twice as far." Andeep says, "Oh, of course, yeah.

And you would travel 20 miles in half an hour." I'd like you to write down as many other facts as you can if you know that the speed that something is travelling is 40 mph, 40 miles per hour.

Pause the video and write down as many as you can.

Give yourself maybe two minutes to do that.

Like I said, you can pause the video now and when you come back we'll take a look at some examples of some things that you may have written.

Pause the video now.

How many did you get? Wow, that's good.

Let's have a look then at some examples.

These are just examples.

Remember, they're an infinite number of facts that we could come up with using 40 miles per hour.

The ones I've written here and shared with you are: we would do 120 miles in three hours, we would do 10 miles in 15 minutes, we would do 60 miles in 1.

5 hours or one and a half hours.

And those are just a few examples of some facts that we can glean from 40 miles per hour.

We can represent this in a ratio table as we are essentially dealing with a unit ratio of hours and that's time to distance.

We've got our time and our distance in miles, 40 mph miles per hour means we travel 40 miles in one hour.

We can now see where Sofia got the 80 from.

We travelled twice as long, so therefore we're gonna travel twice the distance.

So it's a ratio table and you are really familiar with using ratio tables in many different situations and this is just another one place where we can use a ratio table.

We can also see how Andeep came up with the fact that we would travel 20 miles in 30 minutes.

We can see that we have divided the amount of time by two, so therefore we would divide the distance by two, giving us 20 miles in 30 minutes or half an hour.

We can use the ratio table to work out how far you will travel in 4.

5 hours.

I'd like you to pause the video and have a go at using this ratio table to work out how far you travel in 4.

5 hours.

Pause the video.

When you come back, we'll take a look at how Sofia and Andeep have done it and we'll see whether you've done it the same way or maybe you've chosen a different way.

Like I said, pause the video now and then come back when you're ready.

I'm wondering how you did it.

Let's take a look at how Sofia and Andeep did it and see whether your method is the same.

Sofia's workings are here.

She's got 4.

5 hours.

Well, that's equal to two hours + another two hours + 30 minutes, and we know that in two hours we can go 80 miles.

So 80 + 80 plus in 30 minutes we can go 20 miles given a total of 180 miles.

Andeep has chosen to work out like this.

4.

5 hours is one hour multiplied by 4.

5 hours.

We know that in one hour we can go 40 miles, so he's multiplied 40 by the number of hours that we're travelling for, 4.

5, giving 180 miles.

I'm wondering if you chose to do it either of those ways or maybe a different way.

You could have added together four lots of 40 or done four multiplied by 40 and then added on the 20.

That's just another way you could have answered this question.

I'd like you to think now about whose method is more efficient though.

Andeeps method is more efficient, although Sofia's method may be more useful if we were not using a calculator.

The world record for the a hundred metres was set in 2009 by Usain Bolt and was 9.

58 seconds.

What was his average speed? Sofia says, "We would not give this speed in miles per hour as metres are metric and miles are imperial.

So, we would have to give it in kilometres per hour." Andeep says, "I do not think that giving the speed in kilometres per hour is sensible." Can you think of a more appropriate unit to give Usain's speed in? A more appropriate unit would be metres per second.

Let's set up a ratio table.

We know that Usain covered 100 metres in 9.

58 seconds.

So here is my ratio table representing the time and the distance.

We want to know how far he went in one second.

So I've divided by 9.

58.

We know how to use a ratio table.

This gives us 10.

4.

Sofia says, "How can we tell the speed from this table?" And Andeep's response is, "We will give the speed in metres per second.

Which means for every one second." Sofia says, "Oh yes! So his speed was 10.

4 metres per second?" "Yes, that's right.

And we write this as 10.

4 m/s." So we write metres per second as m/s.

The Australian tiger beetle is one of the fastest running insects in the world relative to its body size.

This has been recorded at 6.

8 kilometres per hour, which is 171 body lengths per second.

Wow, that is insane.

Sofia says, "I timed myself doing a five kilometre run at the weekend.

It took me 40 minutes.

I wonder how my speed compares to this beetle?" What do you think? Do you think she's faster or slower than the beetle? Let's calculate Sofia's speed.

We know that Sofia has run five kilometres in 40 minutes.

What units do you think we will measure Sofia's speed in? We will measure Sofia's speed in kilometres per hour and this is represented by the unit km/h.

This means we need to find out how far she goes in one hour.

Therefore, what can we now add to our ratio table? We can add in the 60 because we know that 60 minutes is equivalent to one hour and we want to know how far she goes in one hour because our speed is measured in kilometres per hour.

We're looking for that multiplicative relationship.

Remember, if it's not obvious, we could do 60 divided by 40 giving us the multiplicative relationship of 1.

5.

5 multiplied by 1.

5 is 7.

5.

Sofia ran at an average speed of 7.

5 kilometres per hour.

Sofia says, "My speed was 7.

5 kilometres per hour.

I was faster than the beetle!" Did you think she was gonna be faster than the beetle 'cause I didn't.

I thought the beetle was going to be faster.

Andeep's dad takes him to a karate competition.

The venue is 48 miles from their house and the journey takes one hour and 20 minutes.

What was their average speed? We can see here Sofia's workings and Andeep's workings.

I'm gonna ask you to pause a moment and just look through those two sets of workings to see if you can see what they've done.

Just pause the video, look through and then come back when you're happy with what they've done.

Now, I'd like you to think about whose answer is correct, Sofia's or Andeep's.

Sofia's answer is correct.

Can you see what mistake Andeep has made? He has written 1 hour 20 minutes as 1.

2 hours and this is incorrect as there are 60 minutes in an hour, not 100.

That's a really common mistake.

Here's Andeep's workings, his incorrect workings.

Let's now correct his mistake.

Then 1 hour 20 minutes in hours.

Write it as 1 and then 20 minutes outta the second hour so outta 60 1 and 20 sixtieths.

To get from one and 20 sixtieths to one I divide by one and 20 sixtieths, so I'm going to divide 48 by one and 20 sixtieths giving me 36.

That's the correct answer.

Now, Andeep's answer matches with Sofia's.

We can see Sofia's workings, we can now see Anddeep's corrected workings.

Whose method do you prefer? Sofia says, "This is why I always work in minutes so that I don't have to worry about converting a time given in hours and minutes." We can see that Sofia's workings, she used time in minutes whereas Andeep chose time in hours.

Notice they also decided to write their tables the other way around.

One start had time on the left and the other had time on the right.

It doesn't matter which way round you decide to draw your ratio table.

Andeep says, "I think I'll be doing that from now on, Sofia." A quick check now then.

You may use the calculator.

I'd like you to match each scenario with its correct speed.

Pause the video and then come back when you're ready.

Let's check those answers.

The first one, 75 kilometres in one hour 30 minutes is equivalent to 50 kilometres per hour, 60 kilometres in one hour 20 minutes is 45 kilometres per hour, 36 kilometres in 45 minutes is 48 kilometres per hour, and 180 kilometres in two hours 15 minutes is 80 kilometres per hour.

Here, we have a distance time graph of a cycle ride that Jacob took.

We're going to work out his average speed for the first part of the journey.

Average speed, we're going to be looking at kilometres per hour.

What distance was the first part of the journey? First part of the journey, here, I've highlighted and we can see that the distance is 12 kilometres.

Let's put that into our ratio table.

How long did the first part of the journey take? And we can see the first part of the journey took 40 minutes.

Let's put this into our ratio table.

We're calculating the average speed in kilometres per hour, hence the reason I've put 60 in my time column.

I'm now looking for that multiplicative relationship multiplied by 1.

5, 12 multiplied by 1.

5 is 18.

Jacob's average speed was 18 kilometres per hour.

Your turn now.

I'd like you, please, to work out the average speed for the final part of the journey.

Pause the video, work that out and come back when you are done.

Final part of the journey is highlighted here.

That was 30 minutes and a distance of 15 kilometres.

So, slightly easier this one because our multiplier is two to get to one hour 60 minutes, so that is 30.

The average speed for the final part of the journey was 30 kilometres per hour.

Now then we're ready for task A.

I'd like you please to calculate the speed for each of the following.

Pause the video, work out your answers and then come back when you're ready.

And question number two, pause the video, work out the answers to these questions and come back when you're ready.

Well done.

Here are your answers.

Pause the video, check them and then come back when you're ready.

And question number two.

Again, pause the video, check your answers, and then come back and we'll move on to that second learning cycle.

How did you get on? Great work.

Now, like I said, we can move on to that second learning cycle.

So we're going to look at problems involving speed.

The average speed of a helicopter is 160 miles per hour.

How far can it travel in one hour 45 minutes? Here is our ratio table.

We know we want to work out how far we're going in one hour 45 minutes, which is 105 minutes.

So, we're using Sofia's method of always having everything in minutes.

Andeep says, "What other information can we put into our ratio table? We need three pieces of information in order to find the fourth." Sofia says, "Remember mph means miles per hour." "Oh yes!" Andeep says, "So in one hour you travel 160 miles." Sofia says, "Yes, so we can fill in 60 in the time column and 160 in the distance column." Now we're just missing one piece of information, so we're looking for that multiplicative relationship multiply by 1.

75, multiply by 1.

75 at the distance, we get 280.

A helicopter travelling at a speed of 160 miles per hour will travel 280 miles in one hour and 45 minutes.

The average speed of a cruise ship is 40 kilometres per hour.

The distance between Southampton and Reykjavik is approximately 2,600 kilometres.

How long will it take to sail from Southampton to Reykjavik? And we need to give our answer in days and hours.

We know the speed is 40 kilometres per hour, so this time I've decided to use hours because I've got to give my answer in days and hours, so it might be a little bit unwise here to start with minutes.

We know the distance between the two places is 2,600.

We're looking for that multiplicative relationship.

If I'm not sure, I'm gonna do 2,600 divided by 40 and I can see that relationship is multiplied by 65.

I'm gonna do the same here.

The question, however, asks for our answer in days and hours.

There are 24 hours in a day, so we're going to take our 65 hours and divide by 24 and that gives me this decimal.

I'm then going to take my 65 hours, subtract the total hours in two days, which is two lots of 24, and that gives me a remainder of 17.

It would take two days and 17 hours to sail between Southampton and Reykjavik.

Sofia's mum takes her to a race which is 40 kilometres from their house.

They will travel at an average speed of 50 kilometres per hour.

They need to register for the event at 9:30.

What is the latest time they can leave home and be there on time? Here is my ratio table.

Just want you to think a moment.

Will it be best to use minutes or hours in this question? So, in the previous two examples, I used minutes in one and I used hours in the other.

What do you think would be best to use here? Well, looking at the distance and the speed, we can see that it's going to take less than an hour, so therefore it'd be best to use minutes.

Gonna use minutes.

We know the average speed is 50 kilometres per hour, so in 60 minutes we're going to travel 50 kilometres and it's that multiplicative relationship.

Multiply by 0.

8, multiply by 0.

8, get 48.

The journey will take them 48 minutes.

They need to register for the event at 9:30.

What time will they need to leave home? When 9:30 subtract 48 minutes is 8:42.

They need to leave home at 8:42.

Their average speed was less than 50 kilometres per hour because of traffic.

How will this affect our answer? They would need to leave earlier.

If they're travelling at a slower speed, they would need to leave earlier.

Let's have a go at one question together and then you can have a go at the one on the right hand side independently.

The average speed of a cruise ship is 40 kilometres per hour.

The distance between two places is 3000 kilometres.

How long will it take to sail this distance? And we're going to give our answer in days and hours.

Our speed, in one hour we're travelling 40 kilometres and the distance between the two places is 3000.

My multiplicative relationship is multiplied by 75, meaning is going to take us 75 hours.

We're going to divide that by 24 and we can see here that means we're gonna go three whole days and then part of a day.

So I'm going to do 75 subtract three lots of 24.

That will give me how many hours in the three days and that leaves me with a remainder of three hours.

It would take three days and three hours.

Now your turn, the average speed of a cruise ship is 40 kilometres per hour.

The distance between two places is 3,600 kilometres.

How long will it take to sail this distance? And again, please give me your answer in days and hours.

Pause the video, when you've got your answer come back.

Let's check that answer.

We've got the speed is the same, so one and 40, 3,600.

My multiplicative relationship is multiplied by 90, multiplied by 90.

Then I'm gonna divide by 24.

I can see that it's three whole days and 0.

75 on fourth day.

I'm going to do 90 subtract three lots of 24 so I know how much of time is remaining.

It would take three days and 18 hours.

Now, you're ready to have a go at task B.

Pause the video, answer this question and then come back when you're ready.

And question number two.

Again, pause the video and come back when you're ready.

Question number three.

Again, pause the video, when you're ready come back.

And now question number four.

And how did you get on? There was some quite interesting information in some of those questions, wasn't there? Question number one, the answer is 6.

25 hours or you may have written that as six hours and 15 minutes.

Number two, the bird can fly 510 kilometres in those three hours.

Question three was 20 times.

I don't know about you, but that seems insane to me.

The common swift has gone up in my estimations looking at this question.

And question number four.

A: No, you will not make it on time and it will be five minutes late.

Moving on then to our final learning cycle and we're going to look at pace.

Sofia said, "Earlier, we worked at my speed for completing a five kilometre run.

We could do this because we knew how long it took me.

Whilst I am running, I use pace rather than speed." Andeep says, "I thought speed and pace were the same thing." Do you know what the difference is between speed and pace? Speed is a unit ratio of distance per time period and pace is a unit ratio of time per unit distance.

So, a subtle difference between the two.

Sofia says, "In order for me to complete my park run in my time of 40 minutes I need to maintain a pace of one kilometre per 8 minutes." And Andeep says, "I can see why this is much more useful to you." Sofia keeps a pace of eight minutes per kilometre.

Andeep runs at a speed of 7.

1 kilometres per hour.

Who is running faster? Let's take a look and see at how Sofia and Andeep have answered this question.

Here is Sofia's ratio table and here is Andeep's ratio table.

Sofia says, "I was faster!" Andeep says, "No, I was faster.

My answer is higher than yours." Who is correct? Who do you think is correct? It's Sofia.

Sofia is correct.

She was faster.

Andeep was right.

His answer was higher, but why does that not mean he was faster? Sofia says, "When looking at pace rather than speed, a lower value shows you are running faster." Andeep says, "Of course! You were running a kilometre every eight minutes and I was running one every 8.

45 minutes." Sofia was definitely running faster.

When comparing speed and pace, you can convert between them.

It is really important to consider carefully what your values are showing.

Which is faster? And you're going to have a go at this question yourself.

30 miles per hour or a pace of one mile every one and a half minutes.

Pause the video, make your decision and make sure that you've got all of the workings to support your answer.

There are two ways that you could answer this question.

You could convert the mph into a pace or you could convert the pace into a speed miles per hour.

If we look at the first table that's showing that it takes two minutes to run every mile, and we compare that to one and a half minutes per mile, meaning the pace was quicker.

Looking at the second table, we can see that a pace of a mile every one and a half minutes is equivalent to 40 miles per hour, which is clearly faster than 30 miles per hour.

Now task C.

I'd like you to pause the video, answer these questions and then come back when you're ready.

Well done on those.

Let's check those answers for you.

Question number one, the answer is 12 metres per second.

I've given you there both tables.

It is not necessary to draw both of them you just need to decide which one of those you prefer.

Question two, it was 40 kilometres per hour.

That was faster.

Question three, a pace of one mile per 50 seconds was faster.

Summarising the learning from today's lesson.

Speed is the rate at which something is moving.

It is measured as the distance travelled per unit of time.

The main units of measurement of speed are mph (miles per hour) km/h (kilometres per hour) and m/s (metres per second).

Pace is the rate of movement.

It is measured as the time taken per unit of distance.

Ratio tables are an excellent way to solve problems involving speed and pace.

And there's an example there of the question we looked at earlier with the speed of the helicopter.

Maybe after this lesson you could now pose the question about the common swift and how many times it can fly around the earth, and see if anybody gets vaguely close to the correct answer of roughly 20 times.

Thank you again for joining me and take care of yourself.

Goodbye.