Video: AQA GCSE Mathematics Foundation Tier Pack 2 • Paper 1 • Question 23

Julie drives to a local park to walk her dog. She parks in the car park. She spends 5 minutes in the car park getting ready. She then walks at a constant speed away from her car for 15 minutes. She then turns around and walks at a faster constant speed back to the car park. Julie drew the following distance–time graph to represent her walk. Identify two mistakes in her graph.

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Video Transcript

Julie drives to a local park to walk her dog. She parks in the car park. She spends five minutes in the car park getting ready. She then walks at a constant speed away from her car for 15 minutes. She then turns around and walks at a faster constant speed back to the car park. Julie drew the following distance–time graph to represent her walk. Identify two mistakes in her graph.

So in order to solve this problem and work out what the mistakes are, what I’m gonna do is take a look at each step. So first of all, we can see that Julie spends five minutes in the car park getting ready. Well, therefore, it’s the label for the 𝑦-axis which is important. Because the label for the 𝑦-axis tells us that the 𝑦-axis is the distance from the car park. So if she was in the car park, then the distance from the car park would be zero. So therefore, the first five minutes should be on the 𝑥-axis because it should be at zero distance or zero miles from the car park. So therefore, mistake one is that the line between zero and five minutes should show a distance of zero miles from the car park. As, again, I’ve shown here in orange.

Now let’s continue and see what the second mistake is. Well, the next stage is for Julie to walk a constant speed away from her car for 15 minutes. So we’re not told her speed. So therefore, we can assume this stage of the graph is correct because it’s showing that there is a constant speed. And we know that because it’s a straight line. And if it’s a straight line in a distance-time graph, then it’s constant speed. And we can see that it’s getting further away from the car park which is what we were looking for. And it lasts for 15 minutes. So this section would be correct.

So now, let’s look at the final section. It now says that Julie turns around and then walks at faster constant speed back to the car park. So let’s look at each step of this. So it says that she walks at faster constant speed. Well, when we’re looking at a distance–time graph, the slope or gradient of the line or how steep the line is determines how fast or slow the speed is. So we know that she’s walking at a faster constant speed. So therefore, we want this section of the graph to be a steeper line. And in fact it is, because this section is steeper or has a greater gradient. So therefore, this is correct. It is showing a faster speed.

Next, it says a constant speed. Again, as we’ve mentioned already, a constant speed means we should have a straight line. So it is a straight line. So, so far so good. It’s a faster constant speed. So next, it says back to the car park. Well, if she’s travelling back to the car park, that means that her distance from the car park would be decreasing. And it would decrease eventually to zero because she’d arrive back at the car park. Because, again, if we check the 𝑦-axis, it isn’t distance travelled. Because if it was distance travelled, then yes it would be correct that the graph would be moving further away, because she’s travelling further or covering a further distance. But it is not; it is distance from car park. So if she’s travelling back towards the car park, this will decrease.

And I’ve illustrated how this might have looked on a correct graph. So therefore, Julie’s second mistake is that the line between 20 and 30 minutes should go down to zero miles. So we’ve now solved the problem because we’ve found both the mistakes that Julie has made.

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