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

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Manager
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Martha takes a road trip from point A to point B. She drives [#permalink]  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
Manager
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Re: Average Speed from ManhattanGmat [#permalink]  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.
Intern
Joined: 13 Jun 2007
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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
Manager
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For some reason i get "B"
Manager
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Re: Average Speed from ManhattanGmat [#permalink]  13 Dec 2007, 11:11
E for me.

What's the OA?
Manager
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Agree with E.
Time consuming ...
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