Fill in the gap: __________ is a measure of how fast something is travelling.

Fill in the gap: speed involves two other measures, distance and __________.

A car is travelling at a speed of 20 kilometres per hour. How far will it travel in three hours?

A car travels 90 kilometres in two hours. What is its average speed in kilometres per hour (km/h)?

Binh cycles 80 kilometres in 5 hours. What is her average speed in kilometres per hour (km/h)?

Speed as rate

﻿Hi, I'm Miss Kidd-Rossiter and I'm going to be taking today's lesson on speed, distance and time. It's going to build on the work that we've already done on distance time graphs. Before we get started, make sure you've got something to write with and something to write on. You're in a nice, quiet place, free from all distractions and that you are fully concentrating and ready to go. If you need to pause the video now, to sort any of that out, then please do. If not, let's get going. So for today's try this activity then, Binh and Yasmin are discussing how quickly they can walk to school. Binh says, if I walk 50% faster, I'll get that in 50% of the time. And Yasmin is not sure that that's right. Who do you agree with and why? Pause the video now and have a go at this task. If you're struggling a little bit, it might help you to try some different numbers for the speed or the time and work that way. So pause now and give that a go. Excellent work, well done. Let's think about one example together. So let's say that Binh walks at eight miles per hour. So that's her speed. And let's say that the distance is two miles. Now we know from our work last lesson, that speed is the rate of change of distance. So if she's walking eight miles per hour and she's walking two miles, then that means the time taken will be a quarter of an hour won't it, or 15 minutes. So let's now think about her statement if she walks 50% faster. So what's 50% of eight? Excellent, four. So if she's adding that onto her speed, she'll now be walking at what speed? Tell me. Excellent, 12 miles per hour. So now she's walking at 12 miles per hour. The distance hasn't changed. So because we know that the speed is the rate of change of distance or the distance per unit of time. We know that this must be a sixth of an hour, mustn't it? Two miles, 12 miles per hour. So it's one-sixth of an hour. What is one-sixth of an hour in minutes? Tell me now. Excellent. 10 minutes. So is 10 minutes, 50% faster than 15 minutes. No, it's not is it because 50% of the time would be seven and a half minutes and it's taking us 10 minutes. So I think I agree with Yasmin here. Are there any examples that we can find where it does work? I'll leave you with that. So the connect part of the lesson then, this graph represents the journey of two cars. Which car is travelling more quickly? How do you know? So if you remember from last time, we know that the speed is the rate of change of distance. So we know that the red car, which is this one here, is travelling 250 kilometres in 2.5 hours. So how do we find out what it would be in one hour? Excellent, we divide by 2.5, don't we. So 250 divided by 2.5 is 100 kilometres in one hour. So the speed of the red car is 100 kilometres per hour. The blue car then is also travelling 250 kilometres but in five hours. So if we wanted to work out how much it would be in one hour, how far it would travel, I should say, what would that be? Excellent, it would be 50 kilometres, wouldn't it? Because we divide by five. So we know that the blue car is travelling at 50 kilometres per hour. So the red car is travelling more quickly. How could we have told that from the graph? Excellent. We could say that the gradient or the steepness of the line is bigger. So the red car has a steeper line, so that must mean it's travelling quicker. So as we looked at in our last lesson, speed can be thought of as the distance travelled in one unit of time. And as you've seen from some of the examples that we've done, speed can be calculated by doing the distance travelled, divided by the the time taken. So pause the video here and note that down, cause that's really important. Excellent. So you've now got an activity here. Three of these formulae are correct. Can you explain why? Pause the video now and have a go at this task. Excellent work, well done. Let's go through. So we know that speed is equal to distance divided by time, cause we've just looked at that one together. Which other two are correct? So the first one that's correct is this one here. Distance is equal to speed multiplied by time. And then the final one is this one here. Time is equal to distance divided by speed. Let's go through why this is the case together. So if we know that speed, I'm just going to give speed the letter S for now, is equal to distance, which I'm going to give the letter D, divided by time, which I'm going to give the letter T, so we know that speed equals distance divided by time. We can rearrange this formula, can't we, to figure out one of the others. So let's first look at making distance, the subject of the formula. So here's our distance. So to make distance the subject of the formula, we would need to multiply by time on both sides. So that would give us that speed times time equals distance, which was one of the formulae you noticed was correct. So I'm just going to write that out in full, so that you can also write it down into your notes. Speed multiplied by time equals distance. And then if we start with that formula this time, so I'm just going to write it the other way round. Distance equals speed, times time, then how would we work out time? Excellent. We would divide by speed wouldn't we on both sides. So that gives us that distance divided by speed equals time. So again, I'm just going to write this in full, so you can copy it down. Time is equal to distance divided by speed. So make sure you've got all three of those formulae written in your notes. So this one here, this one here, if you want to write distance equals speed times time, that's absolutely fine. And this one here, because you're going to need those now when you move on to the independent task. So pause the video here, navigate to the independent task. And when you're ready to go through some answers, resume the video. Good luck. Excellent work on that independent task. Let's go through it together then. So the first one we are working out speed aren't we? So we know from our work in the connect task, that speed is equal to distance divided by time. So you're doing your distance, which is a hundred metres divided by your time, which is four seconds. And that gives you an answer of 25 metres per second. And it said in the question, remember to give the correct unit. So our answer there is a metres per second. And then we're working out speed. So we're doing the distance divided by the time. So the distance this time is 260 kilometres and the time is five hours. So our answer is going to be in kilometres per hour, and we get an answer of 52 kilometres per hour. The third one is how long? So how long indicates that we're working out the time and we know to get the time we do the distance divided by the speed. So here, our distance is 42 kilometres and our speed is six. So we'll get an answer of seven hours. So pause the video now, if you need to double check any of you're working. Excellent. Cala runs at nine kilometres per hour for half an hour. How far does she run? So how far indicates that we're using distance. Distance is equal to speed multiplied by time. We have our speed here in kilometres per hour. So that means that we have to write half an hour in hours. So 30 minutes, we have to write that in hours. And we know that 30 minutes is 0.5 hours. So to get the distance, we do nine multiplied by 0.5 and we get our answer of 4.5 kilometres. Xavier drives for 60,000 metres at an average speed of 40 kilometres per hour. So let's just notice something there. His journey starts at 9:50, at what time does his journey end? So if we're asked what time does his journey end, then we've got to work out the time, haven't we? Cause we've got the distance and we've got the speed. So we're working out time, which we know is distance divided by speed. Now we've got to do something here first haven't we? Because we've got metres and kilometres. So we need to first convert 60,000 metres into kilometres, which is what? Excellent, 60 kilometres. So now we have that, we can do our distance, which is 60 kilometres divided by our speed, which is 40 kilometres per hour, and we get our time as 1.5 hours. Now we haven't actually answered the question yet. We've worked out the time that his journey takes, but we're asked what time does his journey end? So we have to add on an hour and a half to 9:50 AM. So 9:50, add one hour is 10:50 AM, isn't it? And then we need to add on half an hour, which takes us to 11:20 AM. So that's our answer for that one. Newcastle University is 285 miles from London. You can either travel direct or travel via Leeds. Compare the two journeys. What are the average speeds? Well, the average speed for travelling direct was 90 miles per hour because you did the distance, which is 285 miles divided by the time taken. So from 13:23 to 16:33, which is three hours and 10 minutes. And three hours and 10 minutes is three and one-sixth hours because 10 minutes is one-sixth of an hour. So when you did this calculation, you needed to use three and a sixth for the time to get your speed. And then here you have to work out the total time before you could calculate the speed. And the speed rounded to the nearest whole number was 81 miles per hour here. So the average speed was faster if you travelled direct. Why would we talk about average speed? Well, clearly they don't travel at 90 miles per hour for the full journey. When the train sets off, it starts slower until it reaches its speed. If it's stopping anywhere, it will slow down. So at some parts of the journey, the train is probably travelling faster than 90 miles per hour, and at some parts of the journey, the train is probably travelling slower than 90 miles per hour. And similarly here there's a 10 minute wait, which means that for 10 minutes, the train isn't travelling at all. Getting on to the explore task now then. How could you complete Binh's sentence in different ways using the cards? So if I increase my speed by percentage, I'll get there in a fraction of the time. Can you spot a pattern? Pause the video now and have a go at this task. Excellent. What did you come up with? There were lots of things to notice here. So let's do one example together. If I increase my speed by 50%, I'll get there two-thirds of the time. Now, if we're increasing by 50%, that's 150%. And 150% as a fraction is? Excellent, three over two. Can you notice anything about three over two and two-thirds? Interesting. If I increase my speed by 20%, I'll get that in five-sixth of the time. So there wasn't a card for that one. You had to use this question mark one. And similarly 20% increase is 120%, isn't it. Which as a fraction is six-fifths. Can we notice anything? Let's do one more together. If we increase by 60%, the speed, we'll get there in five-eighths of the time. So this would be 160%, which we know as a fraction is 16 over 10, which simplifies to eight over five. So again, we've got something going on here. So what did you notice? If we use a multiplier for the speed, then the effect on the time is the reciprocal. And that is because we are dividing by the speed to calculate the time. That's the end of today's lesson. So thank you very much for all your hard work. Don't forget to go and take the end of lesson quiz, so that you can show me what you've learned. And hopefully I'll see you again soon. Bye.

Which of the following calculations can be used to work out speed?

Becky runs at 7 km/h for half an hour. How far does she run?

Ella cycles 18 miles in one and a half hours. What is her average speed in miles per hour?

A train travels 75 miles at an average speed of 25 mph. How long does the journey take?

On the first part of the journey a car travels 160 km in 3 hours. On the second part of the journey the car travels 140 km in 2 hours. What is the average speed of the car over the whole journey?

Calculating speed, distance and time

In this lesson, we will learn to calculate and interpret speed, distance and time.

Maths

Y8 Maths

Key Stage 3

Year 8

Miss

Ratio, real life graphs, and rates of change

Ratio and proportion

THEME

UNIT

Understanding rate

Conversion rates

Exchange rates with graphs

Density as rate

Speed as rate (distance-time graphs)

Displacement-time graphs (Part 1)

Displacement-time graphs (Part 2)

Pete is painting the walls of his bedroom. So far he has used 5 litres of paint and covered 24 m² of wall. What area will 20 litres cover?

Amara is going on holiday. For every £15 she exchanges, she will receive $19. How much money will she get if she exchanges £112.50?

Lesson overview:Calculating speed, distance and time

Core Content

Ratio, real life graphs, and rates of change: