Train A and Train B are traveling in the same direction Trai

Train A and Train B are traveling in the same direction. Train A is traveling 120 mph, Train B is traveling 150 mph. If train A leaves the station at 2:30am, and Train B leaves the same station at 5:30am, what time will Train B catch up to Train A?

Solution

Train A DATA:
rate = 120 mph ; distance = x miles ; time = d/r = x/120 hrs.
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Train B DATA:
rate = 150 mph ; distance = x miles ; time = x/150 hrs
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Equation:
time A - time B = 3 hrs.
x/120 - x/150 = 3
(150x - 120x) = 3*120*150
30x = 360*150
x = 360*5
x = 1800
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Time for B to catch A: 1800/150 = 12 hrs.
Clock time will be 5:30 PM