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A hiker walking at a constant rate of 4 miles per hour is pa

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A hiker walking at a constant rate of 4 miles per hour is pa [#permalink] New post 09 Nov 2010, 06:01
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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 & waits for the hiker 5 min 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
[Reveal] Spoiler: OA
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Re: a hiker walking at a constant rate [#permalink] New post 09 Nov 2010, 06:09
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anilnandyala 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 & waits for the hiker 5 min 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

i am getting 25 how it is 20


In 1/12 hours (5 minutes) after the hiker is passed by the cyclist the distance between them will comprise (20-4)*\frac{1}{12}=\frac{4}{3} miles (note that during these 5 minute hiker walks too, so their relative rate is 20-4 miles per hour). The hiker thus will need \frac{\frac{4}{3}}{4}=\frac{1}{3} hours, or 20 minutes to catch up.

Answer: C.
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Re: a hiker walking at a constant rate [#permalink] New post 09 Nov 2010, 07:42
Cyclist travelled for 5 mins (1/12 hours) before stopping.

Distance between Cyclist & hawker= (1/12)*(20-4) = 4/3 miles.

Hawker should cover this distance with 4 hours/mile = (4/3)/(4/1)= 1/3hour = 20 minutes.

Answer:- C
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Re: a hiker walking at a constant rate [#permalink] New post 09 Nov 2010, 07:48
cyclist is relatively 4times faster
So in 5 minutes, he has taken the lead for 20 minutes relative to the Hiker.

So he has to wait for 20 minutes
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Re: a hiker walking at a constant rate [#permalink] New post 09 Nov 2010, 08:16
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Hiker's speed : Cyclist's speed = 4 : 20 = 1 : 5
To cover the same distance, Time taken by Hiker : Time taken by Cyclist = 5 : 1

(If distance is same, speed is inversely proportional to time)

If cyclist took 5 mins, Hiker will take 25 mins. So she will need another 20 mins. (When cyclist was covering the distance in 5 mins, the Hiker was also walking for those 5 mins)
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Re: A hiker walking at a constant rate of 4 miles per hour is pa [#permalink] New post 14 Oct 2013, 06:39
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Re: A hiker walking at a constant rate of 4 miles per hour is pa [#permalink] New post 15 Oct 2013, 19:23
anilnandyala 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 & waits for the hiker 5 min 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




The cyclist is traveling at a pace of 1 mile every 3 minutes. The hiker is traveling at a pace of 1 mile every 15 minutes.

The cyclist passes the hiker, and then 5 minutes later stops, so they are \frac{5}{3} of a mile from the point they passed the hiker. The hiker is \frac{1}{3}of a mile past the spot where they were passed. \frac{5}{3} - \frac{1}{3} = \frac{4}{3}of a mile, this is how far ahead the cyclist is from the hiker while they wait. since the hiker takes 15 minutes per mile, it will take \frac{4}{3}*15=\frac{60}{3}=20 minutes to catch up to the cyclist.
Re: A hiker walking at a constant rate of 4 miles per hour is pa   [#permalink] 15 Oct 2013, 19:23
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