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# Word problem - average speed

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Intern
Joined: 26 Feb 2011
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Word problem - average speed [#permalink]

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27 Feb 2011, 11:53
00:00

Difficulty:

45% (medium)

Question Stats:

64% (01:54) correct 36% (00:39) wrong based on 22 sessions

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A car traveled 75% of the way from town A to town B by traveling at T hours at an average speed of V mph. The car travels at an average speed of S mph for the remaining part of the trip. Which of the following expressions represents the average speed for the entire trip?

A/ .75V+.25S
B/ .75T+.25S
C/ VT/3S
D/ 4VT/((T+S)/3)
E/ 4VS/ 3S+V
[Reveal] Spoiler: OA
Director
Status: Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing.
Affiliations: University of Chicago Booth School of Business
Joined: 03 Feb 2011
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Re: Word problem - average speed [#permalink]

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27 Feb 2011, 12:18
Let distance AB = 100 miles

75 miles @ V mph, time = 75/V
25 miles @ S mph, time = 25/S

Average speed = 100 / [75/V + 25/S] = 4VS/ 3S+V

A car traveled 75% of the way from town A to town B by traveling at T hours at an average speed of V mph. The car travels at an average speed of S mph for the remaining part of the trip. Which of the following expressions represents the average speed for the entire trip?

A/ .75V+.25S
B/ .75T+.25S
C/ VT/3S
D/ 4VT/((T+S)/3)
E/ 4VS/ 3S+V
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Re: Word problem - average speed [#permalink]

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27 Feb 2011, 12:34
Let the distance between A and B be x.

T = 3/4* x/V
x = 4VT/3

Remaining distance = 0.25* VT/0.75 = VT/3

v_{avg} = Total Distance/(Time taken to travel 75%+Time taken to travel 25%)

$$v_{avg} = \frac{4VT}{3(T+\frac{VT}{3S})}$$

$$v_{avg} = \frac{4V}{3(1+\frac{V}{3S})}$$

$$v_{avg} = \frac{4VS}{(3S+V)}$$

Ans: "E"
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Re: Word problem - average speed   [#permalink] 27 Feb 2011, 12:34
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