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A car traveled 75% of the way from town A to town B by traveling at T

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Joined: 26 Feb 2011
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A car traveled 75% of the way from town A to town B by traveling at T [#permalink]

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27 Feb 2011, 10:53
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Question Stats:

68% (02:04) correct 32% (01:55) wrong based on 111 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. 0.75V + 0.25S
B. 0.75T + 0.25S
C. VT/(3S)
D. 4VT/(T+S)/3
E. 4VS/(3S+V)
[Reveal] Spoiler: OA

Kudos [?]: 123 [1], given: 1

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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
Posts: 863

Kudos [?]: 409 [0], given: 123

Re: A car traveled 75% of the way from town A to town B by traveling at T [#permalink]

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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

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

Kudos [?]: 409 [0], given: 123

Math Forum Moderator
Joined: 20 Dec 2010
Posts: 1946

Kudos [?]: 2175 [0], given: 376

Re: A car traveled 75% of the way from town A to town B by traveling at T [#permalink]

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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: A car traveled 75% of the way from town A to town B by traveling at T [#permalink]

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01 Dec 2016, 08:20
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Re: A car traveled 75% of the way from town A to town B by traveling at T [#permalink]

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02 Dec 2016, 02:36
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. 0.75V + 0.25S
B. 0.75T + 0.25S
C. VT/(3S)
D. 4VT/(T+S)/3
E. 4VS/(3S+V)

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Kudos [?]: 139405 [0], given: 12789

Re: A car traveled 75% of the way from town A to town B by traveling at T   [#permalink] 02 Dec 2016, 02:36
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