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

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

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New post 23 Aug 2016, 13:21
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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. \(x=\frac{2y}{3}\)
[Reveal] Spoiler: OA

Last edited by arabella on 24 Aug 2016, 02:21, edited 1 time in total.
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Re: A train traveled from City A to City B without stopping. The train [#permalink]

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New post 23 Aug 2016, 14:23
What is OA? Is it B?

Avg Speed = Total Distance / Total Time

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

y = 12/7*x
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Re: A train traveled from City A to City B without stopping. The train [#permalink]

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New post 09 Nov 2017, 00:28
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Can anyone explain in more detail about the solution?
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Re: A train traveled from City A to City B without stopping. The train [#permalink]

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New post 09 Nov 2017, 07:42
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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.

Answer: B.
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Re: A train traveled from City A to City B without stopping. The train [#permalink]

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New post 09 Nov 2017, 18:56
Thank you Bunuel
it's clear already.

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.

Answer: B.
Re: A train traveled from City A to City B without stopping. The train   [#permalink] 09 Nov 2017, 18:56
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A train traveled from City A to City B without stopping. The train

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