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## Rates and Distance

tagged by: Brent@GMATPrepNow

This topic has 3 expert replies and 0 member replies
singhmaharaj Senior | Next Rank: 100 Posts
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#### Rates and Distance

Tue May 06, 2014 5:17 am
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

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Brent@GMATPrepNow GMAT Instructor
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Tue May 06, 2014 5:20 am
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

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GMATGuruNY GMAT Instructor
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Tue May 06, 2014 5:28 am
Quote:
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?

1.6 2/3
2.15
3.20
4.25
5.26 2/3
Rate and time are RECIPROCALS.
The RATE RATIO = hiker : cyclist = 4:20 = 1:5.
Thus, the TIME RATIO = hiker : cyclist = 5:1.
The implication is that the hiker will take 5 TIMES AS LONG as the cyclist to travel the same distance.
Thus, when the cyclist passes the hiker, the hiker will then require 25 minutes to travel the number of miles traveled by the cyclist in 5 minutes.
Time difference = hiker's time - cyclist's time = 25-5 = 20 minutes.
Thus, the cyclist will have to wait 20 minutes for the hiker to catch up.

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Jeff@TargetTestPrep GMAT Instructor
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Mon Dec 18, 2017 5:56 pm
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 hikerâ€™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

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