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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...

Expert replies
by BTGmoderatorLU » Tue Mar 31, 2020 6:09 pm

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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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Source: — Problem Solving |

BTGmoderatorLU wrote:
Tue Mar 31, 2020 6:09 pm
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
From the given information, we know that the police is to cover 50 miles driving at a relative speed of 80 – 50 = 30 mph

Time to cover 50 miles = 50/30 hour = 1 hour 20/30*60 minutes = 1 hour 40 minutes

The correct answer: C

Hope this helps!

-Jay
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BTGmoderatorLU wrote:
Tue Mar 31, 2020 6:09 pm
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

Answer: C

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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BTGmoderatorLU wrote:
Tue Mar 31, 2020 6:09 pm
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
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

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