Good PS question. I got it wrong in a hurry : PS Archive
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# Good PS question. I got it wrong in a hurry

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Good PS question. I got it wrong in a hurry [#permalink]

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28 Jan 2006, 01:01
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Hey guys,

I took the GMAT prep today and this was the last Maths question. I thought I had it nailed but it turns out to be a bit tricky.

Q: 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 continues to walk at her constant rate. How many minutes must the cyclist wait until the hiker catches up?

1. 20/3
2. 15
3. 20
4. 25
5. 80/3
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28 Jan 2006, 01:13
the cyclist has passed in 5 minutes 16/12 miles. So he is 4/3 miles ahead of the hiker. The hiker will need (4/3)/4 mph or 4/12 hours which is 20 min
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28 Jan 2006, 01:16
Is it C? 20 minutes.

After 5 minutes of cyclist crossing the walker distance between them is

= Distance travelled by cyclist - distance travelled by walker
= 20/12 - 4/12 = 16/12 = 4/3 miles.

Time taken by walker to travel this distance = (1/4) * (4/3) = 1/3 hours = 20 minutes.
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SAID BUSINESS SCHOOL, OXFORD - MBA CLASS OF 2008

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28 Jan 2006, 03:06
Bingo. You guys are set to crack the GMAT. I forgot to take into account that in the five minutes the hiker would have also walked. Hence got 25. Its amazing what the pressure of time can do to you.
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28 Jan 2006, 03:31
Cyclist continues for 5 minutes. This puts him at 5/60 * 20 = 5/3 miles
Hiker will need (5/3)/(4) = 5/12 hour = 25 minutes to cover this distance, but we need to discount the extra 5 minutes the cyclist took. So this puts it at 20 minutes.
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29 Jan 2006, 17:30
consider the moment the cyclist passes the hiker as the beginning of time.
The cyclist stops and waits for the hiker after 5 mins. At this point they have traveled-
Hiker, who is traveling at 4 mph(4 miles every 60 mins):
4/60 * 5 = 20/60 = 1/3 of a mile

Cyclist is traveling at 20 mph (20 mi every 60 min):
20/60 * 5 = 100/60 = 5/3 of a mile

the distance between them is 5/3 - 1/3 = 4/3 of a mile.

At 4 mph it will take the hiker (4/3)/4, or 1/3 of an hour to meet the cyclist.
1/3 of an hour = 20 mins
29 Jan 2006, 17:30
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