A gang of criminals hijacked a train heading due south. At exactly the same time, a police car located 50 miles north of

[Gmat_mission]

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

Answer: C

Source: Manhattan GMAT

[deloitte247]

The initial gap between the police car and train = 50 miles
Speed of the train = 50 miles per hour
Speed of the police car = 80 miles per hour
Rate of decrease = police car speed - train speed
Rate of decrease = 80 mph - 50 mph = 30 mph
Time taken to close the gap = distance / (speed/decrease rate)
= 50 miles / 30 mph = 5/3 hours
$$\ =1\frac{2}{3}hour\ =\ 1\ hour\ 40\ minutes$$
Answer = C

[Scott@TargetTestPrep]

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

Answer: C

Solution:

Since the police car travels 80 - 50 = 30 mph faster than the criminals, the distance between the police and the criminals decreases 30 miles every hour. Since they were 50 miles apart and time = distance/rate, the police car will catch up to the train in 50/30 = 5/3 hours, or 1 and ⅔ hours. Since ⅔ of an hour is 40 minutes, the police car will catch up to the train 1 hour and 40 minutes.

Answer: C