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
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.