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# A gang of criminals hijacked a train heading due south. At e

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A gang of criminals hijacked a train heading due south. At e [#permalink]  18 Jun 2018, 14:56
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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 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
[Reveal] Spoiler: OA

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Re: A gang of criminals hijacked a train heading due south. At e [#permalink]  19 Jun 2018, 22:57
sandy 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

Sandy please, can you provide the explanation for this?
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Re: A gang of criminals hijacked a train heading due south. At e [#permalink]  21 Jun 2018, 09:35
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The distance is 50 mile.

Train speed is 80.

police speed is 50

Remember - whenever there is a chase - the speed are substracted to find the rate at which the gap is shrinking- here

80-50 = 30

We need to find Time=

Distance
---------
Speed

50/30*60(hour)=
1.40 hour

annswer is C
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Re: A gang of criminals hijacked a train heading due south. At e [#permalink]  10 Jul 2018, 05:29
Expert's post
Explanation

In this “chase” problem, 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 the D = RT formula to find the time:

50 = 30t
$$\frac{5}{3} = t$$

The time it takes to catch up is $$\frac{5}{3}$$ hours, or 1 hour and 40 minutes.
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Re: A gang of criminals hijacked a train heading due south. At e [#permalink]  10 Jul 2018, 12:11
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sandy 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

When elements compete, SUBTRACT THEIR RATES.

The rate for the police = 80 mph, while the rate for the gang = 50 mph.
Thus, every hour the police travel 80 miles, while the gang travels only 50 miles.
The difference between their rates = 80-50 = 30 mph.
Implication of this rate difference:
Every hour the police travel 30 more miles than the gang.
As a result, every hour the police CATCH-UP by 30 miles.

Since the police must catch up by 50 miles, and their catch-up rate is 30 mph, we get:
$$Catch-up-time = \frac{catch-up-distance}{catch-up-rate} = \frac{50}{30} = \frac{5}{3}$$ hours = 1 hour and 40 minutes.

[Reveal] Spoiler:
C

Alternate approach:

MAP OUT the distances in 30-minute increments until the police have traveled the same total distance as the gang.
Since the gang's rate = 50 mph, the gang travels 25 miles every 30 minutes.
Since the police's rate = 80 mph, the police travel 40 miles every 30 minutes.

Start --> gang = 50 miles, police = 0 miles
30 minutes later --> gang = 50+25 = 75 miles, police = 0+40 = 40 miles
1 hour later --> gang = 75+25 = 100 miles, police = 40+40 = 80 miles
1.5 hours later --> gang = 100+25 = 125 miles, police = 80+40 = 120 miles
2 hours later --> gang = 125+25 = 150 miles, police = 120+40 = 160 miles

Since the police are 5 miles behind after 1.5 hours (120 miles for the police versus 125 miles for the gang) but 10 miles ahead after 2 hours (160 miles for the police versus 150 miles for the gang), the time for the police to catch up must be between 1.5 hours and 2 hours.
Only C works.
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Re: A gang of criminals hijacked a train heading due south. At e [#permalink]  10 Jul 2018, 19:08
To simplify:
The range between a police car and a train: 50 miles
The difference in 2 vehicles speed: 30 miles/hour
=> In 1 hour, the range reduces 30 miles. Then only 20 miles are left after 1 hour, obviously it does not need to take a full 1 hour to reduce 20 miles range. Only need: (20/30)* 60mins = 40 mins
The answer is: 1hour + 40 mins
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Re: A gang of criminals hijacked a train heading due south. At e [#permalink]  18 Nov 2018, 21:06
Can anybody explain with picture/ diagram ?
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Re: A gang of criminals hijacked a train heading due south. At e [#permalink]  06 Apr 2019, 07:41
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sandy 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

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

Cheers,
Brent
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Re: A gang of criminals hijacked a train heading due south. At e   [#permalink] 06 Apr 2019, 07:41
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