stonecold wrote:

A gang of criminals hijacked a train heading due south. At exactly the same time, a police car located 50 miles north of the train started driving south toward the train on an adjacent roadway parallel to the train track. If the train traveled at a constant rate of 50 miles per hour, and the police car traveled at a constant rate of 80 miles per hour, how long after the hijacking did the police car catch up with the train?

A. 1 hour

B. 1 hour and 20 minutes

C. 1 hour and 40 minutes

D. 2 hours

E. 2 hours and 20 minutes

The two vehicles are moving in the same direction, with one chasing the other.

To determine how long it will take the rear vehicle to catch up, subtract the rates to find out how quickly the rear vehicle is gaining on the one in front.

The police car gains on the train at a rate of 80 - 50 = 30 miles per hour. Since the police car needs to close a gap of 50 miles, plug into D = RT to find the time:

50 = 30t

5/3 = t

The time it takes to catch up is 5/3 hours, or 1 hour and 40 minutes

Hence option C is correct

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