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Two cities X and Y lie on a straight line. Two men P and Q left simult

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Two cities X and Y lie on a straight line. Two men P and Q left simult  [#permalink]

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New post 09 Nov 2010, 12:27
2
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A
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Difficulty:

  65% (hard)

Question Stats:

56% (02:26) correct 44% (02:29) wrong based on 81 sessions

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Two cities X and Y lie on a straight line. Two men P and Q left simultaneously for Y and X from X and Y respectively. P reaches Y and immediately turns around and moves towards X. On reaching X, again he turns around and moves towards Y. This kind of movement continues indefinitely. Q also travels in a similar manner. The distance between X and Y is 1000m and the ratio of the speeds of P and Q is 3:2. Find the distance traveled by P when he meets Q for the fourth time.

A) 4000M
B) 5600M
C) 4800M
D) 4200M
E) 3200M

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Re: Two cities X and Y lie on a straight line. Two men P and Q left simult  [#permalink]

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New post 09 Nov 2010, 14:46
Let's say that P is traveling at a speed of 300 M/H and Q at a speed of 200 M/H, together the speed is 500 M/H.
The meetings:
1. After 2 hours (1000/500). P traveled 600 M.
2. After 4 more hours (2000/2 - P an d Q are now traveling in the oposite way and first need to get to the oposite starting point and than to go back).
P traveled 600*2 M more, sum of 600+1200=1800 M.
3. After 4 more hours (the same explanation as the No. 2). P traveled 600*2 M more, sum of 600+1200+1200=3000 M.
4. After 4 more hours (they begin this section in the same beginning point). P traveled 600*2 M more, sum of 600+1200+1200+1200=4200 M.

So the correct answer is D - 4200M
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Re: Two cities X and Y lie on a straight line. Two men P and Q left simult  [#permalink]

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New post 10 Nov 2010, 07:07
1
Thanks @ nov79,
Just now got a detailed explanation for this. This is in addition to the above explanation.
Let's say that P is traveling at a speed of 300 M/H and Q at a speed of 200 M/H, together the speed is 500 M/H.
The meetings:
1)When P meets Q for the first time, he would have travelled 3/5 (1000) = 600 m. --- First meeting.
2nd , 3rd and fourth meeting.
Between any two consecutive meetings, any two people separated by a certain distance initially, would be together covering twice the initial distance between them, if they start running simultaneously in opposite directions and move to and fro between their initial starting points.
Hence P and Q would have together cover 2000 m between the 2nd and 3rd as well as 3rd and 4th meeting. Therefore P takes 4 hrs to meet 2nd, 3rd and 4th meeting each. So distance travelled in each meeting = 300*4=1200m each.
Total distance P covers when he meets Q for the fourth time = 600+ 1200+1200+1200 = 4200 m
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Re: Two cities X and Y lie on a straight line. Two men P and Q left simult  [#permalink]

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New post 15 May 2017, 19:44
How we determined that P takes 4 hrs to meet 2nd, 3rd and 4th meeting each?

Could some body please explain it a little bit more
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Re: Two cities X and Y lie on a straight line. Two men P and Q left simult  [#permalink]

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New post 19 May 2017, 00:58
(A) X-------------M1--------Y (B) X-------M2---M1----------Y

To reach their first meeting point (M1), P and Q together cover XM1+YM1=XY=1000M but to reach their 2nd meeting point M2, P and Q must first reach Y and X respectively turn back and walk until they meet again. So together they must cover M1Y+M1Y+YM2+XM2 which means they must traverse the distance XY twice after they have met the first time to meet the 2nd time. This applies to each subsequent meeting. So by their 4th meeting, the combined distance traveled by them will be 1000+2000+2000+2000=7000M. Since the ratio of their speeds is 3:2, P will have covered 60% of this distance or 4200M.
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Re: Two cities X and Y lie on a straight line. Two men P and Q left simult  [#permalink]

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New post 19 May 2017, 23:24
Sorry, made a mistake in my previous post. In order to reach the 2nd meeting point P and Q will traverse M1Y+M1X (not M1Y as previously stated) + YM2+XM2.
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Re: Two cities X and Y lie on a straight line. Two men P and Q left simult  [#permalink]

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New post 20 Feb 2018, 13:24
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1
In General:
Let L be the distance between P and Q.(starting from opposite to each other)
At first meet, total distance travelled by P and Q = L
At second meet, total distance travelled by P and Q = 3L
At thrid meet, total distance travelled by P and Q = 5L
At fourth meet, total distance travelled by P and Q = 7L
.
.
goes on

coming back to our question:
total distance travelled by P and Q at 4th meet = 7L = 7000
speed ratio = 3:2
so out of 7000, P would have travelled (3/5)th of 7000 = 4200
Re: Two cities X and Y lie on a straight line. Two men P and Q left simult &nbs [#permalink] 20 Feb 2018, 13:24
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