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gmatt14
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A cop clocks a motorcyclist speeding down the highway at 90 mph. 2 mi 25 Apr 2010, 07:09
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A cop clocks a motorcyclist speeding down the highway at 90 mph. 2 minutes later the cop tears off after him averaging a speed of 120mph. At this rate how long will it take for our friendly copper to catch the speeder?

Correct Answer:
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6 min.
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Silvers
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A cop clocks a motorcyclist speeding down the highway at 90 mph. 2 mi 25 Apr 2010, 08:18
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gmatt14
A cop clocks a motorcyclist speeding down the highway at 90 mph. 2 minutes later the cop tears off after him averaging a speed of 120mph. At this rate how long will it take for our friendly copper to catch the speeder?

Correct Answer: 6 min.

Any suggestions? Please answer step-wise.

BTW: What would be the least known variable? The cop's distance?

HI,
This can be solved by the concept of relative speed


The cop takes off after the speeding car after 2 minutes.

Distance traveled by the car in 2 minutes = Speed * time = 90 * 2/60 = 3 miles

Now speed of cop = 120 mi/hr
Speed of car = 90 mi/hr

Since both are traveling in the same direction their relative speed = 120 - 90 = 30 mi/hr

Distance difference between 2 = 3mi

So time taken for the cop to catch the car = Difference in distance/ relative speed = 3/30 = 1/10 hr = 6 min

Distance traveled by cop = 120* 6/60 = 12 miles

Distance traveled by the car = 90*(6+2)/60 = 12 miles.

Hope this clears all your doubts :)

cheers
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A cop clocks a motorcyclist speeding down the highway at 90 mph. 2 mi 25 Apr 2010, 08:25
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gmatt14
A cop clocks a motorcyclist speeding down the highway at 90 mph. 2 minutes later the cop tears off after him averaging a speed of 120mph. At this rate how long will it take for our friendly copper to catch the speeder?

Correct Answer: 6 min.

Any suggestions? Please answer step-wise.

BTW: What would be the least known variable? The cop's distance?

One suggestion : please put answers in spoilers.
Solution :
in 2 mis, the motorcyclist goes : 3 miles. [ 90/60 * 2]
relative speed = 120 - 90 = 30 mph
At 30 mph rate, 3 miles will be covered in 60/30 * 3 = 6 minutes.
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A cop clocks a motorcyclist speeding down the highway at 90 mph. 2 mi 25 Apr 2010, 08:29
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Another way is just multiply both the speeds with all the options available, whichever gives you the distance traveled by the cop and the car as same is your answer.

But in this case solving the problem will take a lesser time, unless 6 was option A or B :-D
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A cop clocks a motorcyclist speeding down the highway at 90 mph. 2 mi 26 Apr 2010, 14:10
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bike 90 mph = 1.5 miles/ minute
cop 120 mph = 2 miles/ minute

they both go the same distance (d) and bike gets 2 minute head start (t+2) and we'll call cop's time (t)
bike's equation: 1.5(t+2)=d this is R*T=D
cop's equation: 2t=d

we can set their d's equal since that's the point where they meet and we're trying to solve for t

1.5(t+2)=2t
t=6

I know other people explained it. I just wanted to boost my GMAT confidence and give it my own shot. :)
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A cop clocks a motorcyclist speeding down the highway at 90 mph. 2 mi 06 Apr 2023, 05:50
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