Video: Pack 3 • Paper 3 • Question 4

Pack 3 • Paper 3 • Question 4

02:33

Video Transcript

George went for a run. He ran for a distance of 12 kilometers, correct to the nearest 0.5 kilometers. George found that it took him 100 minutes to complete the run, correct to the nearest 20 minutes. Could George’s average running speed have been greater than eight kilometers per hour?

In order to solve this problem, we firstly need to calculate the maximum and minimum distance and the maximum and minimum time. As George ran 12 kilometers to the nearest 0.5 kilometers, his maximum distance would be 12.25 kilometers and his minimum distance would be 11.75 kilometers. These values have a difference of 0.5 kilometers. George ran for 100 minutes, correct to the nearest 20 minutes. This means that his maximum time is 110 minutes and his minimum time is 90 minutes.

George’s average running speed can be calculated using the formula speed equals distance over time. We want to work out if George’s average speed can be greater than eight kilometers per hour. His maximum speed will be calculated by dividing the maximum distance by the minimum time — in this case, dividing 12.25 kilometers by 1.5 hours as 90 minutes is the same as one and a half or 1.5 hours. This gives us an answer of 8.17 kilometers per hour. Therefore, we can say yes, George’s average running speed could have been greater than eight kilometers per hour.

The second part of the question tells us that George later found out that his time of 100 minutes was in fact correct to the nearest three minutes. Discuss how this would affect your answer.

As his time is now correct to the nearest three minutes, this would increase the minimum time from 90 minutes to 98.5 minutes. Increasing this minimum time would decrease the speed. Therefore, George’s maximum possible speed would decrease.

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