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

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

by BTGmoderatorLU » Wed Mar 02, 2022 2:35 am

00:00

A

B

C

D

E

## Global Stats

Source: Manhattan Prep

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 OA is C

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

by [email protected] » Wed Mar 02, 2022 6:25 am
BTGmoderatorLU wrote:
Wed Mar 02, 2022 2:35 am
Source: Manhattan Prep

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 OA is C
This is a shrinking gap question.

Train's speed = 50 miles per hour
Police card's speed = 80 miles per hour
80 miles per hour - 50 miles per hour = 30 miles per hour
So, the gap between the train and the police car DECREASES at a rate of 30 miles per hour

Original gap (aka distance) = 50 miles
Time = distance/rate
So, time to close gap = 50/30 hours
= 5/3 hours
= 1 2/3 hours
= 1 hour and 40 minutes