SOLUTION: Two trains leave the station at the same time, one heading west and the other east. The westbound train travels 16 miles per hour slower than the eastbound train. If the two trains
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-> SOLUTION: Two trains leave the station at the same time, one heading west and the other east. The westbound train travels 16 miles per hour slower than the eastbound train. If the two trains
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Question 1144021: Two trains leave the station at the same time, one heading west and the other east. The westbound train travels 16 miles per hour slower than the eastbound train. If the two trains are 570 miles apart after 3 hours, what is the rate of the westbound train?
Let x be the rate of the slower train, in mph; then the rate of the faster train is (x+16).
The distance traveler by the slower train in 3 hours is 3x miles;
the distance traveler by the faster train in 3 hours is 3*(x+16) miles.
The total distance is the sum of these values
3x + 3*(x+16) = 570 miles.
Simplify and solve for x:
3x + 3x + 48 = 570,
6x = 570 - 48 = 522,
x = = 87.
ANSWER. The slower train rate is 87 mph; the faster train rate is 87+16 = 103 mph.
CHECK. 3*87 + 3*103 = 3*(87+107) = 3*190 = 570 miles. ! Correct !
