rates

First, find the gap created between the hiker and the cyclist in the first phase of the question. Then, find how long it takes the hiker to close the gap.


Hiker: 4 Mph

Cyclist: 20 Mph



the gap between the cyclist and the hiker is the distance created between them during the first 5 minutes after the cyclist passed the biker. To find it, first find the combined rate by subtracting the hiker's speed for the cyclist's:



Combined rate = 20 - 4 = 16 Mph



Calculate the gap with the [Speed * Time = Distance] formula. The speed is the combined rate (16) and the time is 5 minutes (which is 5/60 hours):



16 * 5/60 = d

d = 80/60 = 4/3 miles



Finally, calculate how long it would take the hiker to complete 4/3 miles:



4 * T = 4/3

T = 1/3



1/3 of an hour is 20 minutes, so the correct answer is B

Alternatively:

Speed of walker = 4 m/hr or 4/60 = 1/15 m/min
Speed of Cyclist= 20 m/hr or 20/60 =1/3 m/min

Distance travelled by cyclist in 5 mins = 1/3*5 = 5/3

Therefore the walker needs to travel 5/3 miles

Hence,
5/3 = 1/15(speed of the walker) * time
or
time = 5/3 * 15
time = 25 mins

As the cyclist waits after traveling for 5 mins.

He waits for 25 - 5 = 20 mins.