The speed of train A is 12 mph slower than the speed of trai

The speed of train A is 12 mph slower than the speed of train B. Train A travels 190 miles in the same time it takes Train B 250 miles. Find the speed of each train.

Solution

Train B DATA:
rate = x mph ; distance = 250 miles ; time = d/r = 250/x hrs
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Train A DATA:
rate = x-12 mph ; distance = 190 miles ; time = d/r = 190/(x-12) hrs
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Equation:
time A = time B
190/(x-12) = 250/x
190x = 250(x-12)
190x - 250x = -12*250
-60x = -12*250
x = 50 mph (Train B speed)
x-12 mph = 38 mph (Train A speed)