Mark biked from his house to his friend's house in how many

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Mark biked from his house to his friend's house in how many [#permalink]

25 Oct 2012, 20:44

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Mark biked from his house to his friend's house in how many hours?

(1) Mark bikes at an average speed of 72 blocks per hour.

(2) If Mark could bike an extra 8 blocks for each hour, he would have arrived at his friend's place 1 hour earlier

I got the correct answer (no spoilers!) but if I were to sit down and calculate the answer, how would I do it (I know purpose is not to calculate in DS, but it's really for practice, if anything).

Thanks again.

[Reveal] Spoiler: OA

Last edited by Bunuel on 26 Oct 2012, 04:26, edited 1 time in total.

Renamed the topic and edited the question.

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Re: Bike rates [#permalink]

25 Oct 2012, 21:17

elegan wrote:

Hello,

I'm looking at this question.

Mark biked from his house to his friend's house in how many hours?

1. Mark bikes at an average speed of 72 blocks per hour.

2. If Mark could bike an extra 8 blocks for each hour, he would have arrived at his friend's place 1 hour earlier

I got the correct answer (no spoilers!) but if I were to sit down and calculate the answer, how would I do it (I know purpose is not to calculate in DS, but it's really for practice, if anything).

Thanks again.

Mark bikes at an average speed of 72 blocks per hour.
Mark could bike an extra 8 blocks for each hour = 80 blocks per hour

LCM of 72 & 80 = 720. Time taken by Mark = 720/72 = 10 hrs.

Cheers!
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Re: Bike rates [#permalink]

25 Oct 2012, 23:15

why you took LCM?
to get a distance
can you explain in detial
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Re: Bike rates [#permalink]

25 Oct 2012, 23:41

Aristocrat wrote:

why you took LCM?
to get a distance
can you explain in detial

There is no sense in taking LCM in such problems. if question said he saved 2 hrs riding his bike 15 blocks/hr faster, the solution would go haywire.

to solve such problems:

Let d be the distance and t the time taken in first case. thus t-1 is time taken in second case.

therefore from 1:
t = d/72
and from 2:
t-1 = d/80

combining these:
t-1 = 72t /80
=>80t -80 =72t
=>t= 10 hrs

Hope it helps.
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Re: Bike rates [#permalink]

26 Oct 2012, 01:01

Another way of approaching this problem -

In all cases, if the speed increases by 1/x, the time taken decreases by 1/x+1 (as speed and time taken are inversely proportional to each other).

In this case the increase in speed is 1/9 (Mark's new speed is 72+8=80 blocks per hour, and the increase of 8 blocks per hour is 1/9th of his previous speed).

Therefore the corresponding decrease in time = 1/9+1 = 1/10. This represents 1/10th of the actual time taken.

1/10th of the actual time taken is given as 1 hour. Hence the total time taken is 10 hours.

Hope it helps.

Cheers!

Re: Bike rates [#permalink] 26 Oct 2012, 01:01

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Mark biked from his house to his friend's house in how many

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Mark biked from his house to his friend's house in how many

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