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# ps distance problems cyclist

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18 Jun 2006, 18:22
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PLZ help needed
explain your reasoning and show the equation used
thanks

One cyclist travels from city A to city B at a constant speed of 8 miles per hour. She rests 4 hours in city B, then she goes back to city A walking at 3 miles per hour. It took her 15 hours from start to finish. What is the distance between the two cities?

oa 124
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18 Jun 2006, 18:27
Distance between 2 cities = x miles
Time taken to cycle to City B = x/8 hours
Time taken to walk back to City A = x/3 hours

Total time taken = 15 = x/8 + x/3 + 4
11 = 11x/24
11(24) = 11x
x = 24 miles

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19 Jun 2006, 00:27

Explanation provided by ywilfred is spot on.
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Zooroopa

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19 Jun 2006, 07:49
thanks for your explanations the official answer was 24 Typo great explanation ywilfred
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Re: ps distance problems cyclist [#permalink]

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19 Jun 2006, 09:34
24 miles is the right answer.

Here is one way to work this (thanks originally to rhyme for the style of operation), while it may seem a little long, it's pretty fast and accurate once you get used to it.

Use d = st, let's ignore the 4 hours of rest because it does not count. The real travel time is 11 hours

so,

A B
d x x
s 8 3
t 11-t t

since distance is equal,
8(11-t) = 3t => 88-8t = 3t => 88 = 11t => t = 8
substituting above,

A B
d 24 24
s 8 3
t 3 8

Distance between cities is 24.

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Re: ps distance problems cyclist   [#permalink] 19 Jun 2006, 09:34
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