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A hiker walking at a constant rate of 4mph is passed by a

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A hiker walking at a constant rate of 4mph is passed by a [#permalink] New post 21 May 2007, 04:34
A hiker walking at a constant rate of 4mph is passed by a cyclist traveling in the same direction along the same path at a constant rate of 20mph. The cyclist stops for 5 mins to wait for the hiker 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) 6.67
b) 15
c) 20
d) 25
e) 26.67

Pls explain :)
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Re: Distance [#permalink] New post 21 May 2007, 07:01
ninomoi wrote:
A hiker walking at a constant rate of 4mph is passed by a cyclist traveling in the same direction along the same path at a constant rate of 20mph. The cyclist stops for 5 mins to wait for the hiker 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) 6.67
b) 15
c) 20
d) 25
e) 26.67

Pls explain :)


Are you sure that it says for 5 mins and not after 5 minutes. Because problem doesn't make sense. We don't know how long the cyclist was riding till he stopped.
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 [#permalink] New post 21 May 2007, 09:53
this is a nice question, i just think it is phrased wrong. not overly difficult, but there are lots of answers that one can get if they don't finish the problem all the way or "answer the wrong question" which i am prone to do (it took me 2x to actually answer the question they were asking at first i thought it was 25; and one of my calculations came up with 6.67 as well)


i am going with C, because i think sergey is correct. the cyclist passed the walker and stopped after riding for 5 minutes.

let me know if there is a quicker way to do this problem:

how far did the cyclist travel in 5 minutes?

rt=d

20mph X 1/12 hour = 5/3 miles

how long will it take the walker to catch up?

well the walker already walked 5 minutes at 4mph:

4mph X 1/12 hour = 1/3 miles. that leaves 4/3 miles left to walk.

how long will it take the walker to walk 4/3 miles?

d=rt
4/3=4t
4/3 * 1/4 = t; t= 1/3 hour = 20 minutes

hope this helps!
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 [#permalink] New post 21 May 2007, 15:58
Sorry guys I cannot find the question at the moment to see if a correction would be needed. Anyway, you are right the answer is C. Thanks :wink:
  [#permalink] 21 May 2007, 15:58
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