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?

Question

Sanford

Mathematics

14 April, 02:48

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?

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Answers (1)

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Misael Donovan · Answer 1

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

Step-by-step 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