A freight train and an express train leave towns 390 km apar

A freight train and an express train leave towns 390 km apart, traveling toward one another. The freight train travels 30 km per hr slower than the express train. They pass one another 3 hr later. What are their speeds?

Solution

Freight DATA:
distance = x miles ; time = 3 hrs ; rate = d/t = x/3 mph
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Express DATA:
distance = (390-x) miles ; time = 3 hrs ; rate = (390-x)/3
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Equation:
rate - rate = 30
(390-x)/3 - x/3 = 30 mph
390-x - x = 90
-2x = -300
x = 150 (distance for the freight train(
x/3 = 50 mph (rate for the freight train)
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390-150 = 240 (distance for the express)
240/3 = 80 mph (rate for the express train)