Two cities x and y are 700kms apart.X to Y is a downstream journey on a stream which flows at a speed of 5kmph.Two boats A and B run to and fro between two cities.speed of boat A which starts from city X is 45 kmph,while speed of boat B starting from city Y is 25kmph.In how much time will the two boats meet for the second time?
Answers
Given : Two cities x and y are 700kms apart.
X to Y is a downstream journey on a stream which flows at a speed of 5kmph.
Two boats A and B run to and fro between two cities.
speed of boat A which starts from city X is 45 kmph,
speed of boat B starting from city Y is 25kmph.
To Find :
In how much time will the two boats meet for the second time?
Solution:
X to Y is a downstream journey
Boat A which starts from city X Speed is 45 kmph
Hence Net speed = 45 + 5 = 50 kmph
boat B starting from city Y speed if 25kmph.
Net speed = 25 - 5 = 20 kmph
Meet first after T hrs
=> 50T + 20T = 700
=> 70T = 700
=> T = 10 hrs
Distance covered by boat A = 50 x 10 500 km
Distance covered by boat B = 20 x 10 = 200 km
Further Time taken to Reach X by B = ((700 - 200)/20) = 25 hr
Time taken to reach X by A = Time to reach Y and and then Reach X
from Y to X speed would be 45 - 5 = 40 kmph
= ( (700 -500)/50) + (700/40)
= 4 + 17.5
= 21.5 hrs
21.5 < 25
Hence Boat A will meet B while Boat B is still going to X
Distance covered in 4 + T hrs
Boat B from Y = 200 + (20)(4 + T)
Boat A from Y = 40T
200 + (20)(4 + T) = 40T
=> 280 = 20T
=> T = 14
4 + T = 4 + 14 = 18 Hrs
10 + 18 = 28 Hrs
After 28 hrs Both boat will meet 2nd time
Distance covered by Boat A = 700 + 560 = (14 x 50 + 14 x 40)
Distance covered by Boat B = 560 = ( 28 x 20)
Boat 1st time meet after 10 Hrs
Boat 2nd time meet after 28 hrs
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