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Question: I need help with this problem?

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?

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Answer:

Let the speed of the express train be x km/h
Since the freight train travels 30km/h slower than the express train, the speed of the freight train is (x - 30) km/h.

In 3 hours, the express train will have travelled 3x km, whereas the freight train will have travelled 3(x - 30) = 3x - 90 km.

The two trains pass one another 3 hours later.
This means that both trains covered 390km together in 3 hours.

Thus, we have:
3x + (3x - 90) = 390
6x - 90 = 390
6x = 390 + 90
6x = 480
x = 480 / 6
x = 80

Speed of express train = x km/h = 80 km/h
Speed of freight train = x - 30 km/h = 80 - 30 km/h = 50 km/h

X kms/hr + (X kms/hr + 30kms/hr) = 390 kms/ 3hrs
2X = 130 - 30
X =100 / 2
X = 50

train 1 = 50 kms/hr
train 2 = 50 + 20 = 80 kms/hr
:)