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A hiker walking at a constant rate of 4 miles per hour is pa [#permalink]

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09 Nov 2010, 07:01

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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 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.

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) _________________

Re: A hiker walking at a constant rate of 4 miles per hour is pa [#permalink]

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14 Oct 2013, 07:39

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: A hiker walking at a constant rate of 4 miles per hour is pa [#permalink]

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15 Oct 2013, 20:23

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]

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09 Dec 2014, 21:48

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: A hiker walking at a constant rate of 4 miles per hour is pa [#permalink]

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07 Aug 2015, 02:51

walking guy's speed in miles/min=4/60=1/15. guy in the cycle=20/60=1/3. So it will be = 1/3-1/15=4/3 thats the speed of the cyclist. now how time will it take to cover 4/3 for the walking guy= 4/3/1/15=20

Re: A hiker walking at a constant rate of 4 miles per hour is pa [#permalink]

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31 Aug 2015, 09:46

According to my understanding, when moving in same direction, time taken to chatch is represented by - Initial Diference Btwn them/ Difference of their speeds. And When in opposite direction, time taken to meet is represented by - Initial difference btwn then/ Sum of their speeds.

Since they are moving in same direction, the equation is (4/3)/16 * 60, (4/3)- Distance Btwn them. 16- Diference in their speeds (as they are moving in same direction) 60- converting Hrs into mins. which comes out to be 5.

Can anyone tell where iam going wrong.

gmatclubot

Re: A hiker walking at a constant rate of 4 miles per hour is pa
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31 Aug 2015, 09:46

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