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Trains A and B start simultaneously from stations 300...

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by swerve » Thu Feb 15, 2018 5:07 am
Trains A and B start simultaneously from stations 300 miles apart, and travel the same route toward each other on adjacent parallel tracks. If Train A and Train B travel at a constant rate of 50 miles per hour and 40 miles per hour, respectively, how many miles will Train A have traveled when the trains pass each other, to the nearest mile?

A. 112
B. 133
C. 150
D. 167
E. 188

The OA is D.

Please, can any expert explain this PS question for me? I tried to solve it but I can't get the correct answer. I need your help. Thanks.

I need to determine the combined speed, right? It will be, 50 + 40 = 90 miles per hour.

Then, I know that the total distance is 300 miles. I stuck here.
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by GMATGuruNY » Thu Feb 15, 2018 5:16 am
swerve wrote:Trains A and B start simultaneously from stations 300 miles apart, and travel the same route toward each other on adjacent parallel tracks. If Train A and Train B travel at a constant rate of 50 miles per hour and 40 miles per hour, respectively, how many miles will Train A have traveled when the trains pass each other, to the nearest mile?

A. 112
B. 133
C. 150
D. 167
E. 188
Since A and B travel toward each other, they WORK TOGETHER to cover the 300 miles between them.
When elements work together, ADD THEIR RATES.
The combined rate for A and B = 50+40 = 90 miles per hour.
Of every 90 miles traveled by A and B working together, 50 miles are traveled by A.
Implication:
Train A will travel 50/90 = 5/9 of the 300-mile distance:
(5/9) * 300 = 500/3 ≈ 167 miles.

The correct answer is D.
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by elias.latour.apex » Thu Feb 15, 2018 5:19 am
Since the trains are traveling towards each other, their speeds can be combined to 90 mph. Accordingly, the trains will meet at 300/90 hours, which reduces to 10/3 or 3 1/3 hours.

Since Train A is going at 50 mph, it will have traveled more than 166.7 miles by the time the trains meet. Accordingly (D) is the best answer.
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by Scott@TargetTestPrep » Mon Feb 19, 2018 3:01 pm
swerve wrote:Trains A and B start simultaneously from stations 300 miles apart, and travel the same route toward each other on adjacent parallel tracks. If Train A and Train B travel at a constant rate of 50 miles per hour and 40 miles per hour, respectively, how many miles will Train A have traveled when the trains pass each other, to the nearest mile?

A. 112
B. 133
C. 150
D. 167
E. 188
We can let time of trains A and B = t and create the following equation:

50t + 40t = 300

90t = 300

t = 300/90 = 10/3 hours

So train A will have traveled 50 x 10/3= 500/3 = 166 2/3 miles by the time they passed, which is closest to the answer of 167.

Answer: D

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