Question 72

Shreya hikes up a hill at 5 mph and comes down at 7 mph. If the total time taken for the two-way journey is 3 hours, what is the distance between the hilltop and the foothill?

Solution

Let's assume the distance between the hilltop and the foothill is 'd' miles.

Shreya hikes up a hill at 5 mph and comes down at 7 mph. If the total time taken for the two-way journey is 3 hours.

$$Average\ speed\ =\ \frac{total\ dis\tan ce\ covered}{total\ time}$$

$$\frac{2\times\ 5\times\ 7}{5+7}\ =\ \frac{d+d}{3}$$

$$\frac{2\times\ 5\times\ 7}{12}=\frac{2d}{3}$$
$$\frac{\ 5\times\ 7}{2}=2d$$
$$\frac{\ 35}{4}=d$$
d = 8.75 miles

So the distance between the hilltop and the foothill is 8.75 miles.

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