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Track X is 13 miles ahead of Truck Y, which is travelling

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Track X is 13 miles ahead of Truck Y, which is travelling [#permalink] New post 12 Aug 2011, 14:28
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Track X is 13 miles ahead of Truck Y, which is travelling the same direction along the same route as Truck X. If Truck X is traveling at an average speed of 47 miles per hour and Truck Y is traveling at an average speed of 53 miles per hour, how long will it take Truck Y to overtake and drive 5 miles ahead of Truck X?
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Re: PS - 700 level - trucks [#permalink] New post 12 Aug 2011, 16:52
bschool83 wrote:
Track X is 13 miles ahead of Truck Y, which is travelling the same direction along the same route as Truck X. If Truck X is traveling at an average speed of 47 miles per hour and Truck Y is traveling at an average speed of 53 miles per hour, how long will it take Truck Y to overtake and drive 5 miles ahead of Truck X?



Let the time taken by truck Y to overtake truck X by 5 kms be Z hrs. Now according to question, truck Y is 13 miles behind truck x and after Z hrs it overtakes truck truck X by 5 miles. so in z hrs truck Y will have traveled 18 miles more than truck x. so,

47Z +18 = 53Z

18 =6Z , thus Z = 3 hrs.

so truck Y will take 3 hrs to overtake truck X by 5 miles.
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Re: PS - 700 level - trucks [#permalink] New post 12 Aug 2011, 18:58
Relative speed of Truck Y (wrt speed of X) = 53-47 = 6
Distance Truck Y needs to travel = 13 (distance between X and Y) + 5 (To go 5 miles ahead of X) = 18

So time required = 18/6 = 3 Hours
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Re: PS - 700 level - trucks [#permalink] New post 13 Aug 2011, 06:28
For those who want to learn a more strategic way to solve such problems:

If two objects start moving towards each other in straight line at the same time, their speeds add up. If moving away, subtract their speeds.

Therefore at a given time, X and Y are 13 + 5 = 18 miles apart. Their speeds relative to each other is 53 - 47 = 6mph.
Therefore, they meet in 18/6 hrs = 3 hours.
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Re: PS - 700 level - trucks [#permalink] New post 13 Aug 2011, 11:28
Hi guys, is this a 700 level question?!?! i'm asking it because i've started studying the quantitative section a few days ago but it seams not that tough ah? thanks
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Re: PS - 700 level - trucks [#permalink] New post 14 Aug 2011, 09:18
well, in ''overtake'' problems u need to subtract one speed from another one. to overcome X, Y needs to ride 13+5 miles. so (53-47)t=13+5 6t=18 t=3 h
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Re: PS - 700 level - trucks [#permalink] New post 14 Aug 2011, 09:55
Relative speed = 6 mph => Y gains 6 miles every hour.

Y needs to travel 18 miles more than X. => Y needs to gain 18 miles.

from the above two statements we can say that it will take 3 hours for Truck Y to overtake and drive 5 miles ahead of Truck X.

Answer 3 hours.
Re: PS - 700 level - trucks   [#permalink] 14 Aug 2011, 09:55
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