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# Two men A and B walk from P to Q a distance of 21 km at rates 3 and 4

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Math Expert
Joined: 02 Sep 2009
Posts: 58396
Two men A and B walk from P to Q a distance of 21 km at rates 3 and 4  [#permalink]

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30 Jan 2019, 02:51
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Difficulty:

45% (medium)

Question Stats:

70% (02:30) correct 30% (02:40) wrong based on 74 sessions

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Two men A and B walk from P to Q a distance of 21 km at rates 3 and 4 km an hour respectively. B reaches Q and returns immediately and meets A at R. The distance from P to R is:

A. 14 km
B. 16 km
C. 18 km
D. 20 km
E. 22 km

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Re: Two men A and B walk from P to Q a distance of 21 km at rates 3 and 4  [#permalink]

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30 Jan 2019, 03:18
1
Bunuel wrote:
Two men A and B walk from P to Q a distance of 21 km at rates 3 and 4 km an hour respectively. B reaches Q and returns immediately and meets A at R. The distance from P to R is:

A. 14 km
B. 16 km
C. 18 km
D. 20 km
E. 22 km

distance covered by B = 21+x
distance covered by A = 21-x
they meet at
21+x/4 = 21-x/3
solve for x = 3

so A meet B at 21-3 = 18 km
IMO C
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Re: Two men A and B walk from P to Q a distance of 21 km at rates 3 and 4  [#permalink]

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30 Jan 2019, 08:37
I found a more logical and fast way for me.
5h is approximately the time needed for B to do PQ.
In 5h A arrived at (3*5 km), so A is impossible.
E is impossible too because of 22>21 and in this option, B would not have returned to meet A.
Now they differ from each other just 6 km (from 15 km to 21 km). in 1 more hour, A will be at 18 km and B 21-4= 17km.
So they should have met between 17 and 18 km.
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Re: Two men A and B walk from P to Q a distance of 21 km at rates 3 and 4  [#permalink]

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30 Jan 2019, 09:23
It's a combined rate problem in disguise!

A and B must walk a combined distance of 42 kms before they can meet. B walks a bigger fraction of the distance because of his faster rate. Their combined rate is 7km/ h. If we want to get the distance from P to R, we have to get the distance A walks.

1. Get the time it takes them to meet
D ÷ R = T
42km ÷ 7km/h = T
T = 6 hours

2. Using T, get the distance that A walks until they meet (point R)
R x T = D
3km/hr x 6 hours = 18 kms

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Re: Two men A and B walk from P to Q a distance of 21 km at rates 3 and 4  [#permalink]

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31 Jan 2019, 02:17
Bunuel wrote:
Two men A and B walk from P to Q a distance of 21 km at rates 3 and 4 km an hour respectively. B reaches Q and returns immediately and meets A at R. The distance from P to R is:

A. 14 km
B. 16 km
C. 18 km
D. 20 km
E. 22 km

P---------X----------R----21-X------Q

The total time by A = Total time by B

X/3 = 21/4 + (21-X)/4

X/3 = (42-X)/4

4X = 3*42 - 3X

7X = 3*42.........X =18

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Re: Two men A and B walk from P to Q a distance of 21 km at rates 3 and 4  [#permalink]

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01 Feb 2019, 19:04
Bunuel wrote:
Two men A and B walk from P to Q a distance of 21 km at rates 3 and 4 km an hour respectively. B reaches Q and returns immediately and meets A at R. The distance from P to R is:

A. 14 km
B. 16 km
C. 18 km
D. 20 km
E. 22 km

We can let t = the time, in hours, it takes B to meet A at R. We also must recognize that when they meet at R, together they have walked exactly twice the distance of 21 km (of course, B walks more than 21 km and A walks less than that). Therefore, we can create the equation:

3t + 4t = 2(21)

7t = 42

t = 6

Therefore, A and B both have walked 6 hours when they meet at R. Therefore, the distance from P to R is also the distance walked by A, which is 6 x 3 = 18 km.

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Re: Two men A and B walk from P to Q a distance of 21 km at rates 3 and 4   [#permalink] 01 Feb 2019, 19:04
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