Time and distance

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sudhir3127: Legendary Member; Posts: 829; Joined: Mon Jul 07, 2008 10:09 pmFollowed by: 3 members; Location: INDIA; Thanked: 84 times

by sudhir3127 » Thu Jul 24, 2008 9:29 pm

1.Tom ,Dik and harry started out on a 100 km journey....tom and
harry went by car at the rate of 25 kmph.while Dik walked at the
rate of 5kmph ..after a certain distance harry got off and walked
on at 5 kmph.while tom went back for Dik and got him to the
destination at the same time that haryy arrived....number of hours
required for the trip is...

Answer after some discussion...

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Source: Beat The GMAT — Problem Solving | Thu Jul 24, 2008 9:29 pm

pepeprepa: Legendary Member; Posts: 661; Joined: Tue Jul 08, 2008 12:58 pm; Location: France; Thanked: 48 times

by pepeprepa » Thu Jul 24, 2008 10:14 pm

2 unknowns and 2 equations
The number of hours for the trip is 8

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parallel_chase: Legendary Member; Posts: 1153; Joined: Wed Jun 20, 2007 6:21 amFollowed by: 2 members; Thanked: 146 times

Re: Time and distance

by parallel_chase » Thu Jul 24, 2008 10:21 pm

sudhir3127 wrote:1.Tom ,Dik and harry started out on a 100 km journey....tom and
harry went by car at the rate of 25 kmph.while Dik walked at the
rate of 5kmph ..after a certain distance harry got off and walked
on at 5 kmph.while tom went back for Dik and got him to the
destination at the same time that haryy arrived....number of hours
required for the trip is...

Answer after some discussion...

Is the answer 8 hrs?

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sudhir3127: Legendary Member; Posts: 829; Joined: Mon Jul 07, 2008 10:09 pmFollowed by: 3 members; Location: INDIA; Thanked: 84 times

by sudhir3127 » Thu Jul 24, 2008 10:21 pm

can u please explain ur answer..yeah 8 is right...

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parallel_chase: Legendary Member; Posts: 1153; Joined: Wed Jun 20, 2007 6:21 amFollowed by: 2 members; Thanked: 146 times

by parallel_chase » Thu Jul 24, 2008 10:29 pm

Harry's Time with Tom : x/25
Harry's time walking: (100-x)/5
Total harry's time

Dick's time walking: y/5
Dick's time with Tom: (100-y)/25
Total dick's time

Tom's time with Harry: x/25
Tom's time returning to Dick: (x-y)/25
Tom's time with Dick till destination : (100-y)/25
Total tom's time

All the total timings can be equal to each other since they reach at the same time.

Solve for three equations: answer 8.

Let me know if there is an easier way of doing this.

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pepeprepa: Legendary Member; Posts: 661; Joined: Tue Jul 08, 2008 12:58 pm; Location: France; Thanked: 48 times

by pepeprepa » Thu Jul 24, 2008 10:38 pm

I drew a line with Y the point where Dick jumped into the car and X the point when Harry started walking.
-------------Y----------X-----------

I build equations about the "time" of the different parts of the journey: Time=Distance/Speed

(100-X)/5=(100-Y)/25 + (X-Y)/25
200=3X-Y

Y/5=X/25 + (X-Y)/25
3Y=X

Join the two equations, it gives you Y=25 and X=75
It takes 5 hours for Dick to go till point Y and 3h hours by car fromo Y to X.
The number of hours is 8

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sudhir3127: Legendary Member; Posts: 829; Joined: Mon Jul 07, 2008 10:09 pmFollowed by: 3 members; Location: INDIA; Thanked: 84 times

by sudhir3127 » Thu Jul 24, 2008 11:18 pm

i did exactly the way as u did parallel.... i found it time consuming though..

pepeprepa: Nice way of solving ...

Thanks a lot all...

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pepeprepa: Legendary Member; Posts: 661; Joined: Tue Jul 08, 2008 12:58 pm; Location: France; Thanked: 48 times

by pepeprepa » Fri Jul 25, 2008 12:14 am

You welcome.
I do not see any faster way to solve it, if someone knows...

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Saule: Junior | Next Rank: 30 Posts; Posts: 15; Joined: Sun Jul 20, 2008 6:37 am

by Saule » Fri Jul 25, 2008 12:48 am

Here's another solution.

100/25=4 is total time to cover the distance by car.

But distance covered by the car was twice as long. Therefore 4*2=8

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parallel_chase: Legendary Member; Posts: 1153; Joined: Wed Jun 20, 2007 6:21 amFollowed by: 2 members; Thanked: 146 times

by parallel_chase » Fri Jul 25, 2008 12:59 am

I dont think you can assume the distance covered by car is twice as long or 200km.

Unless you know the exact value of the points where harry got off and dick got on. You cannot assume the distance.

But I like the method posted by pepeprepa its better and faster.

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pepeprepa: Legendary Member; Posts: 661; Joined: Tue Jul 08, 2008 12:58 pm; Location: France; Thanked: 48 times

by pepeprepa » Fri Jul 25, 2008 1:48 am

Saule wrote:Here's another solution.

100/25=4 is total time to cover the distance by car.

But distance covered by the car was twice as long. Therefore 4*2=8

In this case it is true but you know it once you know the distances of X and Y. Or tell us how you know it is twice as long? At least you need a few calculations.

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