"A passenger train traveled 100 miles in the same amount of time it took a freight train to travel 90 miles. The rate of the freight train was 10 miles per hour slower than the rate of the passenger train. Find the rate of the passenger train."

the rate of the passenger train is 100 mph.

Step-by-step explanation:

Let x represent the rate of the passenger train.

The rate of the freight train was 10 miles per hour slower than the rate of the passenger train. It means that the rate of the freight train is (x - 10) mph

The passenger train traveled 100 miles. It means that the time it took travel 100 miles is

100/x

In the same amount of time, it took a freight train to travel 90 miles. It means that the time it took travel 90 miles is

90/(x - 10)

Since the time is the same, then

100/x = 90/(x - 10)

Cross multiplying, it becomes

100(x - 10) = 90x

100x - 1000 = 90x

100x - 90x = 1000

10x = 1000

x = 100 mph

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