Problem Solving

lheiannie07 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

How will i find the best solution in this?

OA D

Since the train A and B together have to complete 300 miles, and the speed to train A is greater than that of train B, train A would cover more distance than that by train B.

The distance 300 miles would be proportionaltely divided in the ratio of their speeds.

Ratio of speeds: 50 : 40 => 5 : 4. Thus, the distance covered by train A = 300*[5/(5 + 4)] = 300*(5/9) = 500/3 = 167 miles.

The correct answer: D

Hope this helps!

-Jay
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BTGmoderatorDC 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

How will i find the best solution in this?

OA D

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