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.