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# A and B walk from P to Q a dsitance of 42 miles at 3mph and

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Senior Manager
Joined: 30 Aug 2003
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A and B walk from P to Q a dsitance of 42 miles at 3mph and [#permalink]  12 Feb 2004, 14:15
A and B walk from P to Q a dsitance of 42 miles at 3mph and 4 mph respectively . B reaches Q returns immediately and meets A at R .Find the distance from P to R..?
14
28
18
36
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shubhangi

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is it 36

If correct exp. will follow

Boy! ( or for that matter madam!!) these questions take more than 3 mins.

Last edited by kpadma on 12 Feb 2004, 14:27, edited 1 time in total.
Senior Manager
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right.. time consuming..
explain.. it plz
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shubhangi

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shubhangi wrote:
right.. time consuming..
explain.. it plz

Break this in to three steps.

Step 1:
Find the location(T) of A when B reaches Q; so for they were travalling in
the same direction.

P----------------T-------- Q
A----->3
B-------->4

Find TQ

Step 2:
A walks towards Q, while B is walking towards A.

T-----R----Q
A-->3
4<------B

Find QR or TR

Step3:
PR = PQ - RQ

Hope this helps!

Last edited by kpadma on 12 Feb 2004, 14:55, edited 1 time in total.
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A and B are moving in the same direction...
B would take 10.5 hours to reach Q...(42/4)
Meanwhile A would have travelled 31.5 miles... (10.5*3)
B turns back....

A
31.5
34.5 (After 1 hour)
36 (After 1/2 hour)

B
42
38 (After 1 hour)
36 (After 1/2 hour)

Vivek.
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Senior Manager
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well, answer is right... but could someone come with any easy method???
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shubhangi

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Well I will continue half way from Vivek's solution. When B has reached the 42 mile mark, A has travelled 31.5 miles. The difference between them is 10.5 miles. 10.5/(add their speeds) * speed of A. So (10.5/7) * 3 = 4.5 miles. So they would meet at 31.5+4.5 = 36 miles. Does it helps Subhangi?
Senior Manager
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yeah.. thanks.......
hey!! Rakesh.. it msut be very early morning there in india.. were u up whole night...??
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shubhangi

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Subhangi! I am in Australia , to be precise in Melbourne now.
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A travels 42-x distance at 3 mph and B travels 42+x at 4 mph
So since they both take the same time

(42-x)/3 = (42+x)/4
so x = 6 They meet at 6 miles from the endpoint
So the distance from start to point R is 42-6 = 36 miles.
Director
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anandnk wrote:
A travels 42-x distance at 3 mph and B travels 42+x at 4 mph
So since they both take the same time

(42-x)/3 = (42+x)/4
so x = 6 They meet at 6 miles from the endpoint
So the distance from start to point R is 42-6 = 36 miles.

More elegant approach
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Anandnk urs is the best approach,exactly same to me.
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# A and B walk from P to Q a dsitance of 42 miles at 3mph and

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