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Word problem - average speed

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Intern
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Joined: 26 Feb 2011
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Word problem - average speed [#permalink] New post 27 Feb 2011, 10:53
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

63% (01:54) correct 37% (00:20) wrong based on 19 sessions
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
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Joined: 03 Feb 2011
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Re: Word problem - average speed [#permalink] New post 27 Feb 2011, 11:18
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

Madelaine88 wrote:
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] New post 27 Feb 2011, 11:34
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, 11:34
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