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waiting time

by Cheese12 » Mon Oct 10, 2011 6:22 am
A hiker walking at a constant rate of 4miles/hr is passed by a cyclist traveling in the same direction along the same path at a constant rate of 20 miles/hr. The cyclist stops to wait for the hiker for 5 mins 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

OA: C
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by Anurag@Gurome » Mon Oct 10, 2011 6:31 am
Cheese12 wrote:A hiker walking at a constant rate of 4miles/hr is passed by a cyclist traveling in the same direction along the same path at a constant rate of 20 miles/hr. The cyclist stops to wait for the hiker for 5 mins 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?
The 'for' in red shouldn't be there.

Relative speed of the hiker and the cyclist = (20 - 4) = 16 miles/hr

After crossing the hiker, the cyclist has covered 16*(1/12) = 4/3 miles more than the hiker in 5 minutes = 1/12 hrs

The hiker will cover this distance in (4/3)/4 hrs = 1/3 hrs = 20 minutes

The correct answer is C.
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by GMATGuruNY » Mon Oct 10, 2011 7:20 am
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by GmatKiss » Mon Oct 10, 2011 7:38 am
Hiker times

60 mins : 4
30 mins : 2
15 mins : 1
5 mins : 0.33

Cyclist times

60 mins : 20
30 mins : 10
15 mins : 5
5 mins : 1.667

So, hiker should take [(0.33 * 5 - (0.33)] subtract the distance travelled by hiker when Cyclist reached the 5 mins point!

so it has to be (0.33*4) or (5 mins * 4 = 20 mins) for hiker to meet cyclist.

IMO: C
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by fcabanski » Mon Oct 10, 2011 11:20 am
Whenever the problem involves catching up or overtaking find the difference between their rates, and the distance that must be overcome.

Often the faster mover overcomes a head start by the slower. But even in that problem, the only important distance is the distance between them.

"A hiker walking at a constant rate of 4miles/hr is passed by a cyclist traveling in the same direction along the same path at a constant rate of 20 miles/hr. The cyclist stops to wait for the hiker 5 mins 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? "

D=RT

What is the difference between their rates? 20 - 4 = 16 miles/hour

What is the distance that must be overcome? It's the difference in their rates (both are moving) in the formula. 16 * 5/60 = 16 * 1/12 = 16/12 = 4/3 mile.

How long will it take the hiker to cover 4/3 mile? Remember, the biker is still, the hiker moves at 4 mph. T = D/R = 4/3 / 4 = 1/3 hour = 20 minutes.
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