Problem Solving

singhmaharaj wrote:A hiker walking at a constant rate of 4 miles per hour is passed by a cyclist travelling 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 continues to walk at her constant rate. How many minutes must the cyclist wait until the hiker catches up?


A) 6 2/3

B) 15

C) 20

D) 25

E) 26 2/3

Here's one approach:

5 minutes after the cyclist passes the hiker
The cyclist is traveling 16 mile per hour faster than the hiker.
Distance = (time)(speed)
Time = 5 minutes = 1/12 hours
So, the distance between them = (16)(1/12) = 16/12 = 4/3 miles

Time for hiker to catch up
Distance = 4/3 miles
Hiker's speed = 4 miles per hour
Time = distance/time = (4/3)/4 = 1/3 hours = 20 minutes = C

Cheers,
Brent

singhmaharaj wrote:A hiker walking at a constant rate of 4 miles per hour is passed by a cyclist travelling 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 continues to walk at her constant rate. How many minutes must the cyclist wait until the hiker catches up?


A) 6 2/3

B) 15

C) 20

D) 25

E) 26 2/3

We are given that a cyclist travels at a rate of 20 mph, passes a hiker, and then stops to wait for the hiker after traveling for 5 minutes. Since 5 minutes = 1/12 hours, the cyclist travels a distance of 20/12 = 5/3 miles.

We let the extra time, in hours, of the hiker = t, and then the hiker's total time is t + 1/12; thus, the distance in miles of the hiker is 4(t + 1/12) = 4t + 1/3.

Since the hiker catches the cyclist, we set their distances equal and determine t:

4t + 1/3 = 5/3

4t = 4/3

t = (4/3)/4 = 4/12 = 1/3 hours = 20 minutes

Answer: C