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GMAT Prep Rates Problem

by tonebeeze » Sun May 22, 2011 1:00 pm
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 kier 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

OA = C
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by smackmartine » Sun May 22, 2011 3:51 pm
IMO C

Both cyclist and hiker are moving in the same direction , so we can take their relative speed. (Relative speed is the speed of one object with respect to the other. We assume that one object is stationary and another is moving. When two objects move in same direction , the relative speed is the difference between their individual speeds. When objects are moving in the opposite direction, the relative speed is the sum of their individual speed.)

So Relative speed is (20-4)m/h = 16 m/hr.

So Distance covered by the cyclist in 5 min or 5/60 hr = (relative speed)* time = 16 m/hr * 5/60 hr = 4/3 miles

To cover this distance, time taken by the hiker will be =

(Distance between hiker and cyclist after 5 min )/Individual speed of hiker = (4/3 miles)/4 m/hr = 1/3 hr = (1/3)*60 min = 20 min

So , C
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by GMATGuruNY » Sun May 22, 2011 4:51 pm
tonebeeze wrote: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 kier 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

OA = C
Since the rate of the cyclist is 20/4 = 5 times the rate of the hiker, the hiker will take 5 times as long to travel the same distance as the cyclist.
The cyclist travels for 5 minutes.
Thus, the hiker needs 5*5 = 25 minutes to travel the same distance.
Since the hiker also has been traveling for 5 minutes when the cyclist stops, the hiker needs 25-5 = 20 more minutes to catch up to the cyclist.

The correct answer is C.
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by peelamedu » Fri Jun 10, 2011 12:44 am
The cyclist stops after 5 mins.
Distance covered in 5 minutes by cyclist = distance covered by hiker in t minutes
20* (5/60) = 5*t
t = 5/12
Time taken by hiker is greater and so cyclist must wait 5/12-5/60 min more which is 1/3. I.e 20 mins.
IMO C
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by Vish_ » Fri Jun 10, 2011 1:16 am
IMO C

Agreeing with GMATGuruNY
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by cans » Fri Jun 10, 2011 6:25 am
H=4mph
C=20mph
in 5 minutes, Distance traveled by C = 5/3 miles
H = 1/3
Thus hiker needs to cover 5/3 - 1/3 = 4/3 miles
time = 20 minutes
IMO C
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