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Martha takes a road trip from point A to point B. She drives

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Martha takes a road trip from point A to point B. She drives [#permalink] New post 10 Dec 2007, 13:49
Martha takes a road trip from point A to point B. She drives x percent of the distance at 60 miles per hour and the remainder at 50 miles per hour. If Martha's average speed for the entire trip is represented as a fraction in its reduced form, in terms of x, which of the following is the numerator?

(A) 110
(B) 300
(C) 1,100
(D) 3,000
(E) 30,000

[Reveal] Spoiler:
E

Last edited by fameatop on 29 Jul 2013, 09:22, edited 1 time in total.
OA not Provided
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Re: Average Speed from ManhattanGmat [#permalink] New post 10 Dec 2007, 14:21
JCLEONES wrote:
Average speed

--------------------------------------------------------------------------------

Martha takes a road trip from point A to point B. She drives x percent of the distance at 60 miles per hour and the remainder at 50 miles per hour. If Martha's average speed for the entire trip is represented as a fraction in its reduced form, in terms of x, which of the following is the numerator?

(A) 110
(B) 300
(C) 1,100
(D) 3,000
(E) 30,000


I get B. Let's call d the total distance from A to B. Then the average speed can be represented as d/time. Further, the time can be represented as the sum of the time spent at 60 mph and the time spent at 50 mph, where time = distance/rate. So the time is:

xd/60 + (1-x)d/50, and the overall equation for average speed is:

speed = d/[xd/60 + (1-x)d/50]. To simplify, first find a common denominator for the two time components:

xd/60 + (1-x)d/50 = 5xd/300 + 6(1-x)d/300 = (6d-xd)/300. So,

speed = d/[(6d-xd)/300]. Rewrite as

speed = d * 300/(6d-xd) = 300/(6-x). So the numerator is 300.
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 [#permalink] New post 10 Dec 2007, 16:40
I find it E.
"johnrb" did not consider that x is in percent so all the equations need to have x/100 and (100-x)/100
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 [#permalink] New post 11 Dec 2007, 13:59
For some reason i get "B"
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Re: Average Speed from ManhattanGmat [#permalink] New post 13 Dec 2007, 11:11
E for me.

What's the OA?
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 [#permalink] New post 13 Dec 2007, 20:30
Agree with E.
Time consuming ...
  [#permalink] 13 Dec 2007, 20:30
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Martha takes a road trip from point A to point B. She drives

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