Estimating a marathon from stride length
Estimating a marathon from stride length
IP 1
7 marks
A marathon is \(42.195\text{ km}\) long. A runner's stride is \(1.18\text{ m}\) long and she takes \(172\) strides per minute.
- By rounding each value to \(1\) significant figure, estimate the number of strides needed to complete the marathon.[2]
- Hence estimate the time taken, in hours, correct to \(1\) significant figure.[2]
- Using a calculator, find the time taken, correct to the nearest minute. State one assumption you have made.[2]
- Comment on why the estimate in part (b) is close to the answer in part (c).[1]
Solution:
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Answer:(a) \(40\,000\) strides (b) \(200\) minutes, about \(3\) hours (c) \(208\) minutes, assuming constant stride length and rate with no stops (d) the roundings act in opposite directions and partly cancel
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