speed problem

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Taniuca: Senior | Next Rank: 100 Posts; Posts: 62; Joined: Mon Aug 02, 2010 3:25 pm; Thanked: 3 times

by Taniuca » Sat Aug 28, 2010 12:06 pm

Truck X is 13 miles ahead of Truck Y, which is traveling 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?

2 hours
2 hours 20 min
2 hours 30 min
2 hours 45 min
3 hours

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Source: Beat The GMAT — Problem Solving | Sat Aug 28, 2010 12:06 pm

kmittal82: Master | Next Rank: 500 Posts; Posts: 324; Joined: Mon Jul 05, 2010 6:44 amFollowed by: 3 members; Location: London; Thanked: 70 times

by kmittal82 » Sat Aug 28, 2010 3:30 pm

Distance between trucks = 13 miles
Relative speed = 53-47 = 6 mph

Time take by Y to catchup to X = 13/6 hours.

Using the same average speed, time take by Y to cover 5 miles = 5/6 hours

Thus, total time taken = 13/6 + 5/6 = 18/6 = 3hours

Can you confirm the OA?

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Taniuca: Senior | Next Rank: 100 Posts; Posts: 62; Joined: Mon Aug 02, 2010 3:25 pm; Thanked: 3 times

by Taniuca » Sat Aug 28, 2010 4:38 pm

kmittal82 wrote:Distance between trucks = 13 miles
Relative speed = 53-47 = 6 mph

Time take by Y to catchup to X = 13/6 hours.

Using the same average speed, time take by Y to cover 5 miles = 5/6 hours

Thus, total time taken = 13/6 + 5/6 = 18/6 = 3hours

Can you confirm the OA?

__-
3 is the right answer, could you then confirm that when using speed problems if we have a car comming against other with the same distance, or one catching another like this problem we should always use relative speed? if so, when do we add or substract on relative speed? any formulas?
thanks!

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Taniuca: Senior | Next Rank: 100 Posts; Posts: 62; Joined: Mon Aug 02, 2010 3:25 pm; Thanked: 3 times

by Taniuca » Sat Aug 28, 2010 4:47 pm

Taniuca wrote:
kmittal82 wrote:Distance between trucks = 13 miles
Relative speed = 53-47 = 6 mph

Time take by Y to catchup to X = 13/6 hours.

Using the same average speed, time take by Y to cover 5 miles = 5/6 hours

Thus, total time taken = 13/6 + 5/6 = 18/6 = 3hours

Can you confirm the OA?
__-
3 is the right answer, could you then confirm that when using speed problems if we have a car comming against other with the same distance, or one catching another like this problem we should always use relative speed? if so, when do we add or substract on relative speed? any formulas?
thanks!

Also, i found that since the distance is equal, I could get the answer T=5/6, like this
47T=d+13
53T= d+18
My issue is that even when I get T=5/6 I don't know how to get 13/6 from the same problem. How would you analize this?

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Sat Aug 28, 2010 6:51 pm

Taniuca wrote:Truck X is 13 miles ahead of Truck Y, which is traveling 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?

2 hours
2 hours 20 min
2 hours 30 min
2 hours 45 min
3 hours

Truck Y is 13 miles behind. We want it to get 5 miles ahead. So Truck Y has to travel 13+5 = 18 more miles than Truck X.

This is a great question for plugging in the answers, which represent the amount of time it will take Truck Y to travel 18 more miles than Truck X. Since 18 is an integer, the correct answer likely will be A or E.

Answer choice E:
Distance X = r*t = 47*3 = 141.
Distance Y = r*t = 53*3 = 159.
Y-X = 159-141 = 18. Success!

The correct answer is E.

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kmittal82: Master | Next Rank: 500 Posts; Posts: 324; Joined: Mon Jul 05, 2010 6:44 amFollowed by: 3 members; Location: London; Thanked: 70 times

by kmittal82 » Sun Aug 29, 2010 9:54 am

Taniuca wrote:
kmittal82 wrote:Distance between trucks = 13 miles
Relative speed = 53-47 = 6 mph

Time take by Y to catchup to X = 13/6 hours.

Using the same average speed, time take by Y to cover 5 miles = 5/6 hours

Thus, total time taken = 13/6 + 5/6 = 18/6 = 3hours

Can you confirm the OA?
__-
3 is the right answer, could you then confirm that when using speed problems if we have a car comming against other with the same distance, or one catching another like this problem we should always use relative speed? if so, when do we add or substract on relative speed? any formulas?
thanks!

Hi,

Yes, if 2 objects are moving towards each you can add their velocities, and if they are moving in the same direction you subtract their velocities. Its a nifty little trick, helps a lot during these types of questions.

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diebeatsthegmat: Legendary Member; Posts: 1119; Joined: Fri May 07, 2010 8:50 amFollowed by: 3 members; Thanked: 29 times

by diebeatsthegmat » Sun Aug 29, 2010 10:25 am

Taniuca wrote:Truck X is 13 miles ahead of Truck Y, which is traveling 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?

2 hours
2 hours 20 min
2 hours 30 min
2 hours 45 min
3 hours

i will solve the problem like this
X Y
speed= 47 53
time = t+13/47 t ( here, t+13/47 because x goes ahead 13 killometers thus x must go sooner than y:13/47 hour)
distance=d d+5
thus we will have x: 47(t+13/47)=d
and y= 53t=d+5
from this equations we will have 47t +13+5=53t and t=3

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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members; Location: New York, NY; Thanked: 39 times

by Jeff@TargetTestPrep » Mon Dec 11, 2017 10:34 am

Taniuca wrote:Truck X is 13 miles ahead of Truck Y, which is traveling 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?

2 hours
2 hours 20 min
2 hours 30 min
2 hours 45 min
3 hours

We have a catch-up-and-pass problem, for which we can use the formula:

change in distance/change in rate = catch-up-and-pass time

We are given that Truck X is 13 miles ahead of Truck Y, and we need to determine the time it takes Truck Y to overtake Truck X by 5 miles. Thus, the change in distance is 13 + 5 = 18 miles.

We are also given that Truck X travels at a constant speed of 47 mph and Truck Y at a speed of 53 miles per hour. Thus, the change in rate is 53 - 47 = 6 mph.

Therefore, the catch-up-and-pass time is: 18/6 = 3 hours.

Answer: E

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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