# Video: AQA GCSE Mathematics Higher Tier Pack 3 • Paper 1 • Question 9

The distance-time graph shows a race. a) Who won the race? Give a reason for your answer. b) The race begins with a flat section followed by a hill. At what distance along the track do you think the hill begins? Give a reason for your answer. c) Describe the race.

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### Video Transcript

The distance-time graph shows a race.

Part a) Who won the race? Give a reason for your answer.

There are several pieces of information that we can deduce from this distance-time graph. Firstly, each of the lines showing the race run by Alistair, Ethan, and Logan stop at 3000 metres. This tells us that it is a 3000-metre race.

We can also find the speed of any of the runners at any point by looking at the gradient of the line. This means that the more steep the graph is, i.e., the higher its gradient, the faster the person is running. And similarly, it means that the less steep the graph is, the slower the person is running. So who won the race?

Well, the person who won the race will be the person who finished it in the shortest amount of time. Well, if we look carefully, we can see that Ethan finished the race in 20 minutes, Alistair finished it in 21 minutes, and Logan finished it in 24 minutes. We can say then that Ethan must have won the race. He ran it in the shortest amount of time.

Part b) The race begins with a flat section followed by a hill. At what distance along the track do you think the hill begins? Give a reason for your answer.

Remember, we said that the gradient of the graph represents the speed. The smaller the gradient, i.e., the less steep the graph, the slower the person is running. We can see at the points marked that Alistair, Ethan, and Logan slow down. The gradient of each of their graphs reduces. We can see that this occurred at 1000 metres. This means the hill must begin at 1000 metres. The gradient of each of the lines, and that represents their speed, decreased at this point.

Part c) Describe the race.

To describe the race, we need to look at what’s happened for each of the runners throughout the race. The first section for Alistair’s graph was the steepest, so he began the race the fastest. If we look carefully, we can see that Ethan overtook Alistair just before the 16-minute mark. So Alistair was in the lead until just before this point. Ethan overtook him at this point, and he led the race until he won. Poor old Logan was in third place throughout the entire race.