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# A train traveled from City A to City B without stopping. The train

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Intern
Joined: 24 Feb 2016
Posts: 27
Location: India
Schools: LBS (A)
GMAT 1: 650 Q45 V34
GPA: 4
A train traveled from City A to City B without stopping. The train  [#permalink]

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Updated on: 24 Aug 2016, 03:21
1
00:00

Difficulty:

35% (medium)

Question Stats:

72% (02:05) correct 28% (01:51) wrong based on 156 sessions

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A train traveled from City A to City B without stopping. The train traveled the first third of the distance from City A to City B at an average speed of x miles per hour, it traveled the next third of the distance from City A to City B at an average speed of 2x miles per hour, and it traveled the final third of the distance from City A to City B at an average speed of 4x miles per hour, where x > 0. The average speed of the train when it traveled from City A to City B was y miles per hour. Which of the following equations correctly gives x in terms of y?

A. $$x= \frac{3y}{7}$$

B. $$x=\frac{7y}{12}$$

C. $$x= \frac{3y}{5}$$

D. $$x=\frac{5y}{8}$$

E. $$x=\frac{2y}{3}$$

Originally posted by arabella on 23 Aug 2016, 14:21.
Last edited by arabella on 24 Aug 2016, 03:21, edited 1 time in total.
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Joined: 03 Jul 2016
Posts: 75
Re: A train traveled from City A to City B without stopping. The train  [#permalink]

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23 Aug 2016, 15:23
What is OA? Is it B?

Avg Speed = Total Distance / Total Time

y = 1/ ((1/3x)+(1/6x)+(1/12x))

y = 12/7*x
Intern
Joined: 02 Feb 2014
Posts: 40
GPA: 3.33
Re: A train traveled from City A to City B without stopping. The train  [#permalink]

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09 Nov 2017, 01:28
1
Can anyone explain in more detail about the solution?
Math Expert
Joined: 02 Sep 2009
Posts: 49271
Re: A train traveled from City A to City B without stopping. The train  [#permalink]

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09 Nov 2017, 08:42
2
1
arabella wrote:
A train traveled from City A to City B without stopping. The train traveled the first third of the distance from City A to City B at an average speed of x miles per hour, it traveled the next third of the distance from City A to City B at an average speed of 2x miles per hour, and it traveled the final third of the distance from City A to City B at an average speed of 4x miles per hour, where x > 0. The average speed of the train when it traveled from City A to City B was y miles per hour. Which of the following equations correctly gives x in terms of y?

A. $$x= \frac{3y}{7}$$

B. $$x=\frac{7y}{12}$$

C. $$x= \frac{3y}{5}$$

D. $$x=\frac{5y}{8}$$

E. $$x=\frac{2y}{3}$$

Assume the total distance to be 3 miles.

Time to cover the first third of the distance at x miles per hour = 1/x
Time to cover the second third of the distance at 2x miles per hour = 1/(2x)
Time to cover the final third of the distance at 4x miles per hour = 1/(4x)

Total time = 1/x + 1/(2x) + 1/(4x) = 7/(4x).

(The average rate) = (Total distance)/(Total time)

y = 3/(7/(4x)) = 12x/7

x = 7y/12.

_________________
Intern
Joined: 02 Feb 2014
Posts: 40
GPA: 3.33
Re: A train traveled from City A to City B without stopping. The train  [#permalink]

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09 Nov 2017, 19:56
Thank you Bunuel

Bunuel wrote:
arabella wrote:
A train traveled from City A to City B without stopping. The train traveled the first third of the distance from City A to City B at an average speed of x miles per hour, it traveled the next third of the distance from City A to City B at an average speed of 2x miles per hour, and it traveled the final third of the distance from City A to City B at an average speed of 4x miles per hour, where x > 0. The average speed of the train when it traveled from City A to City B was y miles per hour. Which of the following equations correctly gives x in terms of y?

A. $$x= \frac{3y}{7}$$

B. $$x=\frac{7y}{12}$$

C. $$x= \frac{3y}{5}$$

D. $$x=\frac{5y}{8}$$

E. $$x=\frac{2y}{3}$$

Assume the total distance to be 3 miles.

Time to cover the first third of the distance at x miles per hour = 1/x
Time to cover the second third of the distance at 2x miles per hour = 1/(2x)
Time to cover the final third of the distance at 4x miles per hour = 1/(4x)

Total time = 1/x + 1/(2x) + 1/(4x) = 7/(4x).

(The average rate) = (Total distance)/(Total time)

y = 3/(7/(4x)) = 12x/7

x = 7y/12.

Re: A train traveled from City A to City B without stopping. The train &nbs [#permalink] 09 Nov 2017, 19:56
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