Video: AQA GCSE Mathematics Higher Tier Pack 2 • Paper 2 • Question 11

Caroline is going to cycle from Brighton to Portsmouth. the distance from Brighton to Portsmouth is 50 miles. She plans to leave at 9:30 am. a) she assumes that she will travel at an average speed of 15 mph. using her assumption work out the arrival time in Portsmouth. b) In fact, Caroline had a greater average speed. How does this affect her arrival time?

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Video Transcript

Caroline is going to cycle from Brighton to Portsmouth. the distance from Brighton to Portsmouth is 50 miles. She plans to leave at 9:30 am. Part a) she assumes that she will travel at an average speed of 15 miles per hour. using her assumption work out the arrival time in Portsmouth.

Since Caroline is assuming an average speed of 15 miles per hour, we can use the formula that relates speed, distance, and time. Speed is equal to distance over time. You might have also seen this represented in triangle form. To work out Caroline’s arrival time, we first need to find the total time it takes her to cycle 50 miles.

She travels a distance of 50 miles, and her average speed is 15 miles per hour. We can substitute these into the formula, and we get 15 is equal to 50 over 𝑡. To solve, we’ll multiply both sides of this equation by 𝑡, to get 15𝑡 is equal to 50.

We’ll then divide through by 15. 𝑡 is equal to 50 over 15. We could work out 50 divided by 15 using our calculator. But notice how both 50 and 15 share a common factor of five. That means 50 over 15 simplifies to 10 over three hours. 10 divided by three is three remainder one. So 10 over three is equal to three and a third of an hour.

There are 60 minutes in an hour. So we can work out how many minutes there are in one-third of an hour by finding one-third of 60. To do that, we divide 60 by three and we get 20. And we can see that the total amount of time it takes Caroline to cycle 50 miles is three hours and 20 minutes.

She sets off at 9:30 am. We first add three hours, and that takes us to 12:30 pm. We then add 20 minutes, and that takes us to 12:50 pm. Using the assumption that she travels at an average speed of 15 miles an hour then, Caroline should arrive in Portsmouth at 12:50 pm.

Don’t forget to include an indication of whether she arrives in the morning or afternoon. In this case, it’s the afternoon, so we add pm.

Let’s just consider what the first step would have looked like had we used the triangle method. We were trying to find the time, so we cover that up in the triangle. 𝐷 is above 𝑠, distance is above time, so that tells us we divide the distance by the time. Distance divided by speed is 50 divided by 15, which is the exact same sum that we did earlier.

Both of these methods are entirely valid This method can be beneficial if you’re not so confident in rearranging equations. Either way, Caroline will arrive in Portsmouth at 12:50 pm.

Part b) In fact, Caroline had a greater average speed. How does this affect her arrival time?

A greater average speed means she’s travelling faster. That means she’ll take less time to travel the same distance. This will mean she will arrive earlier than the original estimated time.

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