Question

A cyclist managed to ride 5 miles against the wind in the same time that it took him to ride 10 miles with the wind. If the wind speed is 4 mph, which equation can be used to calculate the cyclist's average rate of speed in miles per hour

Answer 1

Given that the cyclist rides distances of 5 miles and 10 miles due to the wind, the equation that can be used to calculate the speed is therefore;

$\frac{10}{v + 4} = \frac{5}{v - 4}$

How can the correct equation be found?

The distance the cyclist rides against the wind = 5 miles

The distance the cyclist rides with the wind = 10 miLes

Let t represent the time it took the cyclist in both directions, we have;

$t = \frac{10}{v + 4} = \frac{5}{v - 4}$

Where;

v = The cyclist's average rate of speed

Which gives;

10 × (v - 4) = 5 × (v - 4)

10v - 40 = 5v - 20

5v = 20

v = 20 ÷ 5 = 5

The equation that can be used to calculate the cyclist's average rate of speed is therefore;

$t = \frac{10}{v + 4} = \frac{5}{v - 4}$

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