Question

A hiker walking at a constant rate of 4 miles per hour is passed by a cyclist traveling in the same direction along the same path at a constant rate of 20 miles per hour. The cyclist stops to wait for the hiker 5 minutes after passing her, while the hiker continue to walk at her constant rate. How many minutes must the cyclist wait until the hiker catches up?

Answer 1

Answer: the cyclist must wait for 25 minutes until the hiker catches up.

Explanation:

Distance = speed × time

The Cyclist was travelling in the same direction along the same path

as the hiker at a constant rate of 20 miles per hour. If the cyclist stops to wait for the hiker 5 minutes after passing her, then the distance that the cyclist travelled in 5 minutes(5/60 hour) is

20 × 5/60 = 100/60 miles

For the hiker to catch up with the cyclist, she would cover 100/60 miles at a speed of 4 miles per hour.

Time = distance/speed

Time required by hiker to catch up with the cyclist is

(100/60)/4 = 100/240 hour

Converting 100/240 hour to minutes, it becomes

100/240 × 60 = 25 minutes