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arabella
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A train traveled from City A to City B without stopping. The train Updated on: 24 Aug 2016, 03:21
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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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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45% (medium)

Question Stats:

73% (02:36) correct 27% (02:33) wrong based on 636 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. \(x=\frac{2y}{3}\)
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A train traveled from City A to City B without stopping. The train 09 Nov 2017, 08:42
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arabella
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. \(x=\frac{2y}{3}\)
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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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A train traveled from City A to City B without stopping. The train 23 Aug 2016, 15:23
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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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A train traveled from City A to City B without stopping. The train 09 Nov 2017, 01:28
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Can anyone explain in more detail about the solution?
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A train traveled from City A to City B without stopping. The train 09 Nov 2017, 19:56
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Thank you Bunuel
it's clear already.

Bunuel
arabella
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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A train traveled from City A to City B without stopping. The train 17 Feb 2020, 04:18
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arabella
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. \(x=\frac{2y}{3}\)
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Let’s assume that the total trip is 60 miles, which means that each leg of the trip is 20 miles. Thus the times for the three legs of the trip are 20/x, 20/2x, and 20/4x, respectively.

We can create the following equation for the average speed:

Average Speed = Total Distance / Total time

y = 60 / (20/x + 20/2x + 20/4x)

y = 60 / (20/x + 10/x + 5/x)

y = 60 / (35/x)

y = 12x/7

Solving for x, we obtain;

7y/12 = x

Answer: B
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A train traveled from City A to City B without stopping. The train 19 Jan 2022, 10:22
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Can anyone explain in more detail about the solution?
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Sure!

So I solved the question my using plug-in numbers:

Assume, that we have a distance of 90miles that is travelled and x = 30 mph.

The first third (30miles) is travelled at 30mph, so in 1h.
The second third (30miles) is travelled at 2*30mph, so in 0.5h.
The third third (30miles) is travelled at 4*30mph, so in 0.25h.

Now: the formula for average speed is total distance / total time.

Total distance = 90 miles, total time = 1h + 0.5h + 0.25h = 1.75h

Dividing 90 / 1.75, we will get something around 51; remember, this is our average speed so 51 = y.

Now, you have x = 30 and y = 51 and you can look in the answers which answer fits the values.

And in the end you simply need to look which answer fits these values best. Here it is (B).

Hope it could help you or maybe someone else :)
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A train traveled from City A to City B without stopping. The train 09 Feb 2023, 01:48
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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?

Average Speed = 3ABC/AB + BC + CA
Concept: Applicable when one travels at speed "a" for one-third of the distance, at speed "b" for one -third of the distance and speed "c" for one-third of the distance.
Stem : Average speed from A To B = "Y",
Speed A = X
Speed B = 2X
Speed c = 4X,
Substituting values, \(3(X)(2X)(4X)/(2X*X) +(2X*4X) +(4X*X) \)= Y
\(2X^2(12X)/2X^2(1+4+2)\) = Y
\(12X/7\) = Y
X =\( 7Y/12\)
B
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A train traveled from City A to City B without stopping. The train 21 Aug 2025, 05:56
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