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

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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 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 hijacked 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

Source: Manhattan Prep

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swerve wrote:
Thu Apr 15, 2021 4:52 am
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 hijacked 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

Source: Manhattan Prep
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

Answer: C

Cheers,
Brent
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