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# Francine traveled x percent

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Current Student
Status: mba here i come!
Joined: 07 Aug 2011
Posts: 270
Location: Pakistan
Concentration: Strategy, Marketing
GMAT 1: 680 Q46 V37
GMAT 2: Q V
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Kudos [?]: 622 [1] , given: 48

Francine traveled x percent [#permalink]  26 Aug 2011, 12:28
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Question Stats:

76% (03:49) correct 23% (01:11) wrong based on 21 sessions
During a trip, Francine traveled x percent of the total distance at an average speed of 40 miles per hour and the rest of the distance at an average speed of 60 miles per hour. In terms of x, what was Francine’s average speed for the entire trip?

A. (1800 - x) /2
B. (x + 60) /2
C. (300 - x ) / 5
D. 600 / (115 - x )
E. 12,000 / ( x + 200)

[Reveal] Spoiler: Solution
First, we should assume x = 50, both distances are the same. To find the average speed over the same distance, the equation is: 2*s1*s2/(s1+s2). In this case, that's 2*40*60/100, which is 48.

So, plug 50 back into the choices for x, and look for 48... E works.
[Reveal] Spoiler: OA

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Director
Joined: 01 Feb 2011
Posts: 774
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Kudos [?]: 75 [0], given: 42

Re: Francine traveled x percent [#permalink]  26 Aug 2011, 16:09
distance time

xd/100 40 mph

(100-x)(d/100) 60 mph

Average speed = total distance/ total time

= d/ (xd/4000)+(((100-x)d)/6000)

= 1000 /((x/4) + ((100-x)/6))

= 12000/(x+200)

Current Student
Status: mba here i come!
Joined: 07 Aug 2011
Posts: 270
Location: Pakistan
Concentration: Strategy, Marketing
GMAT 1: 680 Q46 V37
GMAT 2: Q V
Followers: 23

Kudos [?]: 622 [0], given: 48

Re: Francine traveled x percent [#permalink]  26 Aug 2011, 23:39
Total time taken = \frac{xd}{100*40} + \frac{(100-x)d}{100*60}

= \frac{d(200+x)}{12000}

Avg speed = \frac{d*12000}{d(200+x)}

= \frac{12000}{x+200}
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Manager
Joined: 18 Aug 2011
Posts: 60
Followers: 1

Kudos [?]: 7 [0], given: 6

Re: Francine traveled x percent [#permalink]  27 Aug 2011, 05:28
Say the total distance is 100 miles and x is 60

60 miles w/ 40m/h => 60/40 = 3/2 hours
40 miles w/ 60m/h => 40/60 = 2/3 hours

In total = 3/2 + 2/3 = 13/6 hours
Total distance = 100

Avg. speed: 100/(13/6) = 10 * (6/13) = 600/13

Check the answers by plugging in x = 60 and see that for E it is 12000/260, cancel with 2 and 10 and get 600/13 => E it is
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Joined: 31 May 2010
Posts: 38
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Kudos [?]: 1 [0], given: 2

Re: Francine traveled x percent [#permalink]  27 Aug 2011, 11:01
Should be E.

Let distance be 1.

Then avg speed will be 1/ (x/40+1-x/60) = 1200/x+200
Re: Francine traveled x percent   [#permalink] 27 Aug 2011, 11:01
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# Francine traveled x percent

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