Two trains leave the same station at the same time, but are headed in opposite directions. one train travels at 50 miles per hour and the other train travels at 60 miles per hour. how much time passes until the trains are 660 miles apart?

Let n =  the hours elapsed when the two trains are 660 miles apart.

Let the first train travel east and the second train travel west.
The distance traveled by the first train is
x = (50 mi/h)*(n h) = 50n mi

The distance traveled by the second train is
y = (60 mi/h)*(n h) = 60n h

The distance between the two trains after n hours is
x + y = 50 n + 60n = 110n mi

Because this distance is 660 miles, therefore
110n = 660
n = 6 hours

6 hours

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