A train leaves Deb's house and travels at 50 miles per hour. Two hours later, another train leaves from Deb's house on the track beside or parallel to the first train but it travels at 100 miles per hour. How far away from Deb's house will the faster train pass the other train?

You want the distance from Deb's house that a train traveling 50 mph is passed by one that leaves 2 hours later traveling 100 mph.

Distance

As a function of time (t) since the first train left, the distance each train is from Deb's house is ...

first train: 50t
second train: 100(t -2)

The trains will be at the same distance when ...

50t = 100(t -2)
50t = 100t -200 . . . . . eliminate parentheses
200 = 50t . . . . . . . . . . add 200-50t
4 = t . . . . . . . . . . . . . . . divide by 50

The distance each train is from Deb's house 4 hours after the first train left is ...

50(4) = 200 = 100(4 -2)

The faster train passes the first train 200 miles from Deb's house.

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Additional comment

Effectively, the 100 mile head start the first train has is being closed at the rate of 50 mph, the difference in speeds. Thus it takes 2 hours for the gap to close, in which time the second train has traveled 100 mph × 2h = 200 mi.