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A and B walk from P to Q, a distance of 21km at 3 and 4

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Director
Joined: 24 Oct 2005
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A and B walk from P to Q, a distance of 21km at 3 and 4 [#permalink]  04 May 2006, 06:31
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A and B walk from P to Q, a distance of 21km at 3 and 4 km/hr respectively. B reaches Q, and immediately returns and meets A at R. What is the distance btw P and R?
Director
Joined: 16 Aug 2005
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Location: France
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[#permalink]  04 May 2006, 06:54
P------------------------------R-------------Q

let distance between Q and R be x

Distance travelled by A is 21-x
Distance travelled by B is 21+x

time = distance/speed

So,
(21+x)/4 = (21-x)/3
=> 3(21 + x) = 4(21-x)
=> 63 + 3x = 84 - 4x
=> 7x = 21
=> x = 3

So, PR = 18 miles
Manager
Joined: 13 Aug 2005
Posts: 136
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[#permalink]  04 May 2006, 07:07
It would take B 21/4 hours to reach point Q.
During this time A walked 3*21/4 and the difference between the point where he is and Q at the moment A reached Q is 21/4 miles.
Now they are walking toward each other: t - time they spend walking
t*(3+4)=21/4 => t=3/4. B would walk 4*3/4=3miles.
Then the distance is 21-3=18 miles.
Manager
Joined: 13 Dec 2005
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[#permalink]  04 May 2006, 07:51
they totally walked 21*2 =42 miles because B travelled 21 Plus X and A travelled 21 minus X so 42 miles

42 miles at a speed of 7 miles per hr so they walked for 6 hour

A travelled 6 *3 = 18 miles and thats the distance between P & R
Manager
Joined: 14 Mar 2006
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[#permalink]  04 May 2006, 07:53
I find it much easier to do these type of questions with a Chart, its called RDT chart, just a suggestion. Agree with the asnwer.
Senior Manager
Joined: 29 Jun 2005
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[#permalink]  05 May 2006, 03:08
P_______________________T________R___Q
The distance between P and R = PT + TR
B reaches Q in 21/4=5,25 hours. In 5.25 hours A passes 3*5.25=15.75 km PT=15.75
P_________15.75__________T___5.25_R____Q
Then, B starts back, while A is still on its way to Q
The distance between A and B Is 5.25, the speeds are 3 and 4, so we have to do next is to find when they will meet:
5.25/(3+4)=0.75 hour. In 0.75 hour A will pass additional 0.75*3=2.25 km TR=2.25
So the answer is PT+TR=15.75+2.25=18km
Manager
Joined: 27 Mar 2006
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[#permalink]  07 May 2006, 13:19
Agree with 18
[#permalink] 07 May 2006, 13:19
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A and B walk from P to Q, a distance of 21km at 3 and 4

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