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

Question

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

Archit3110 · Accepted Answer

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

tati912 · Answer

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

Answer: 18km. C

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Ben1 · Answer

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.
 Answer C, IMO.

Mo2men · Answer

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

Answer: C

ScottTargetTestPrep · Answer

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.

Answer: C

Kinshook · Answer

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

Asked: The distance from P to R is

B takes time to reach Q = 21/4 = 5.25 hours

A travels in 5.25 hours = 3 * 5.25 = 15.75 km

Let the distance form P to R = x km

Distance covered by A & B in opposite direction = 21 - 15.75 = 5.25 km
Relative speed = 7 kmh

Time required = 5.25/7 
Distance travelled by A = (5.25/7)*3 = 2.25 km

Distance from P to R = 15.75 + 2.25 = 18 km

IMO C

GMATWhizTeam · Answer

Solution: 
 • Distance between P and Q = 21Km
• Time taken by B to reach Q =  \frac{21}{4} = 5.25  hours
• Distance covered by A in 5.25 hours =  5.25*3 = 15.75  Km
 o Difference between A and B =  21 – 15.75 = 5.25  km 
• Now A and B together will cover the distance of 5.25Km, when they will meet at R.
 o Speed of A and B =  3 + 4 = 7  km/hr
o Time taken to cover 5.25Km =  \frac{5.25}{7} = 0.75  hr 
• Distance between P to R = distance covered by A in  6 (5.25 + 0.75)  hours =  6*3 = 18  KM 
Hence, the correct answer is  Option C.

GMATWhizTeam · Answer

Solution:  
When they meet for the first time at point R, 
 • The total distance covered by both of them =  21 + 21 = 42   
 https://www.dropbox.com/s/ekza7w309wxbsb2/29.jpg?dl=1 
Since, they are meeting after the same time "t". 
 • Their speed and distance must be directly proportional.
•  Sa: Sb = 3: 4 
•  Da: Db = 3: 4 
 o Distance covered by A = Da = PR =  \frac{3}{(3 + 4) }* 42 = 18  km  
Hence, the correct answer is  Option C

btsaami · Answer

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:

Time taken for A to reach from P to Q and Q to R = Time for B to reach from P to R
3/4=(21-k)/(21+k)

7k= 21(4-3)
k=3
Hence PR = 21-3= 18 km

bumpbot · Answer

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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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