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Two trains going in opposite directions leave at the same time. Train B travels 25 mph faster than train A. In 6 hours the trains are 690 miles apart. Find the speed of each.
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Let x be the speed of the train A and y be the speed of the train B.
Then
(1) b - a = 25, and
(2) b + a = = 115.
One more time:
(1) b - a = 25, and
(2) b + a = 115.
Add the equations (1) and (2) (both sides). You will get
2b = 25 + 115 ---> 2b = 140 ---> b = ---> b = 70.
Then a = b - 25 = 70 - 25 = 45.
Answer. The train A speed is 45 mph. The train B speed is 70 mph.