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A train travels from Albany to Syracuse, a distance of...

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A train travels from Albany to Syracuse, a distance of...

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A train travels from Albany to Syracuse, a distance of 120 miles, at the average rate of 50 miles per hour. The train then travels back to Albany from Syracuse. The total travelling time of the train is 5 hours and 24 minutes. What was the average rate of speed of the train on the return trip to Albany?

A. 60 miles per hour
B. 50 miles per hour
C. 48 miles per hour
D. 40 miles per hour
E. 35 miles per hour

The OA is D.

The total distance from Albany to Syracuse is, 120 miles, and the train travels at a rate of 50 miles per hour, that's mean that the time that the train spent from Albany to Syracuse is, 120 / 50 = 2.4 hour or 2 hours and 24 minutes.

If we know that the total travelling time of the train was 5 hours and 24 minutes, the time that the train spent from Syracuse to Albany will be, 5.4 - 2.4 = 3 hours.

Now, we can get the average rate of speed of the train on the return trip to Albany, will be 120 / 3 = 40 miles per hour.

Experts, is there another way to solve this PS question? Thanks.

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swerve wrote:
A train travels from Albany to Syracuse, a distance of 120 miles, at the average rate of 50 miles per hour. The train then travels back to Albany from Syracuse. The total travelling time of the train is 5 hours and 24 minutes. What was the average rate of speed of the train on the return trip to Albany?

A. 60 miles per hour
B. 50 miles per hour
C. 48 miles per hour
D. 40 miles per hour
E. 35 miles per hour

The OA is D.

The total distance from Albany to Syracuse is, 120 miles, and the train travels at a rate of 50 miles per hour, that's mean that the time that the train spent from Albany to Syracuse is, 120 / 50 = 2.4 hour or 2 hours and 24 minutes.

If we know that the total travelling time of the train was 5 hours and 24 minutes, the time that the train spent from Syracuse to Albany will be, 5.4 - 2.4 = 3 hours.

Now, we can get the average rate of speed of the train on the return trip to Albany, will be 120 / 3 = 40 miles per hour.

Experts, is there another way to solve this PS question? Thanks.
Hi swerve.

The way you did it is perfect.

Another way that we could do here is the following (but I rather the way you did it):

The total distance is 120*2=240 miles.

The total time is 5 hours and 24 minutes = 5.4 hours.

The average speed is: ( 50 m/h + v_2 m/h ) / 2.

We have to find v_2. Now, using the formula d=v*t, we will get:

$$240\ =\ \frac{\left(50+v_2\right)}{2}\cdot5.4\ \ \Leftrightarrow\ \ 50+v_2\ =\ 88.88889\ \Leftrightarrow\ v_2\ =\ 38.88889\approx39\ \frac{\text{miles}}{\text{hour}}.$$ Now, if we see the options, the right answer is the option D=40.

I hope this answer may help you too.

I'm available if you'd like a follow-up.

Regards.

_________________
GMAT Prep From The Economist
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swerve wrote:
A train travels from Albany to Syracuse, a distance of 120 miles, at the average rate of 50 miles per hour. The train then travels back to Albany from Syracuse. The total travelling time of the train is 5 hours and 24 minutes. What was the average rate of speed of the train on the return trip to Albany?

A. 60 miles per hour
B. 50 miles per hour
C. 48 miles per hour
D. 40 miles per hour
E. 35 miles per hour

We see that it took the train 120/50 = 2.4 hours = 2 hours and 24 minutes to travel from Albany to Syracuse. Since the total time is 5 hours and 24 minutes, it must be true that it took the train 3 hours for the return trip. Since the return trip is also 120 miles, the average speed of the return trip is 120/3 = 40 mph.

Answer: D

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scott@targettestprep.com



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