Speed, Time prob #1

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papgust: Community Manager; Posts: 1537; Joined: Mon Aug 10, 2009 6:10 pmFollowed by: 252 members; Thanked: 653 times

by papgust » Fri Sep 18, 2009 7:49 pm

Hi guys,

Following is a problem that i'm not able to solve.. Please help with a good shortcut solution,

Peter and Paul start simultaneously on 2 different cars from Point A and travel towards Point B at speeds of 52 kmph and 39 kmph respectively on the same road. As soon as Peter reaches Point B, he returns back to Point A on the same road and meets Paul on the way. How far from Point B do the two friends meet, if the distance between the 2 points is 70 kms?

Can someone come up with a shortcut formula/approach for this kind of problem? Appreciate your response!!

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Source: Beat The GMAT — Problem Solving | Fri Sep 18, 2009 7:49 pm

KapTeacherEli: GMAT Instructor; Posts: 578; Joined: Tue Aug 25, 2009 6:00 pmFollowed by: 62 members; Thanked: 136 times

by KapTeacherEli » Fri Sep 18, 2009 8:59 pm

Peter will reach B (70 km) then turn around and meet Paul (x km) who has traveled most of the way to B (70-x km). The total distance that the two of them cover 70 + 70 - x + x = 140.

So the two are covering 140 km of total distance, we need to know at what rate they do so. Since the two of them are moving towards each other, working together, we can combine their speeds. They are closing that 140 km gap at a rate of 52 + 39 = 91 km/hr.

140 km / 91 km/hr = 20/13 hrs. It takes the 20/13 of an hour to move 140 km total distance and meet in the middle.

In 20/13 hrs, at 39 kph, Paul will have traveled (20/13)hrs * 39 kph = 60 km.

Since Paul has traveled 60 km when he meets Peter, he is 70 - 60 = 10 km from point B.

Eli Meyer
Kaplan GMAT Teacher
Cambridge, MA
www.kaptest.com/gmat

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aa2kash: Junior | Next Rank: 30 Posts; Posts: 27; Joined: Thu Jul 23, 2009 6:29 am; Thanked: 3 times

by aa2kash » Sat Sep 19, 2009 3:48 am

thanks Ali for the different and timesaving approach.

I did it with the basic formula, time=dis/speed
since they are meeting after sometime say T. thefore i compared the timetaken by both peter and paul.
70+x is covered by peter and 70-x is covered by paul.

(70+x)/52=(70-x)/39
this gives x=10.

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vivekjaiswal: Master | Next Rank: 500 Posts; Posts: 107; Joined: Tue Sep 15, 2009 7:18 pm; Location: Pune, India; Thanked: 6 times; GMAT Score:630

hmmm that makes so much more sense

by vivekjaiswal » Sat Sep 19, 2009 7:27 am

aa2kash,

that was a clever way...and the quickest way i think
thanks for that solution

Cheers,
Vivek

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papgust: Community Manager; Posts: 1537; Joined: Mon Aug 10, 2009 6:10 pmFollowed by: 252 members; Thanked: 653 times

by papgust » Sun Sep 20, 2009 4:42 am

Thank you Eli and aakash for your nice approach to this problem. I completely got the approach now.

Thank you once again!

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viju9162: Master | Next Rank: 500 Posts; Posts: 434; Joined: Mon Jun 11, 2007 9:48 pm; Location: Bangalore; Thanked: 6 times; GMAT Score:600

by viju9162 » Sun Sep 20, 2009 6:51 am

Hi aa2kash,

You have equated "T" ( time) for both the equations? can it be done ?

The time taken to travel cannot be equal for both peter and paul .. Correct me if I am wrong here?

Regards,
Viju

"Native of" is used for a individual while "Native to" is used for a large group

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aa2kash: Junior | Next Rank: 30 Posts; Posts: 27; Joined: Thu Jul 23, 2009 6:29 am; Thanked: 3 times

by aa2kash » Sun Sep 20, 2009 1:22 pm

@Viju
Its mention in the question that they start simultaneously. It means they when they are meeting they have taken the same time to travel their respective distances.So, we can equate the time taken by both of them.
Hope it clears your query now.

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viju9162: Master | Next Rank: 500 Posts; Posts: 434; Joined: Mon Jun 11, 2007 9:48 pm; Location: Bangalore; Thanked: 6 times; GMAT Score:600

by viju9162 » Mon Sep 21, 2009 3:43 am

Hi aa2kash,

Yep,it clarified. Thank you

"Native of" is used for a individual while "Native to" is used for a large group

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