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A swimming pool is filled with 3 pipes with uniform flow of water.The first two pipes operating simultaneously fill the pool in the same time during which the poo; is filled by the 3 rd pipe alone.The 2 nd pipe fills the pool in 5 hours faster than the 1 st pipe and 4 hours slower than the 3 rd pipe.Find the time required by each pipe to fill the pool seperately?

A swimming pool is filled with 3 pipes with uniform flow of water.The first two pipes operating simultaneously fill the pool in the same time during which the poo; is filled by the 3rd pipe alone.The 2nd pipe fills the pool in 5 hours faster than the 1st pipe and 4 hours slower than the 3rd pipe.Find the time required by each pipe to fill the pool seperately?

Grade:10

1 Answers

Arun
25768 Points
3 years ago
let the volume of the pool = v
let the time taken by second pipe to fill pool = x hours
time taken by first pipe = (x+5) hours
time taken by third pipe = (x –4) hours
 
in one hour,
first pipe can fill V/(x+5)  parts of volume of pool
second pipe can fill V/x  parts of volume of pool
third pipe can fill  V/(x –4)  parts of volume of pool
 
now it is given that
time taken by first ad second pipe simultaneously = time taken by third pipe alone
V/(x+5) V/x = V/(x –4)
1/(x+5) + 1/x = 1/(x –4)
when solving, we get
x2 –8x – 20 = 0
x = 10  or x = –2
neglect x = –2
thus x = 10
 
time taken by second pipe to fill pool = x hours = 10 hours
time taken by first pipe = (x+5) hours = 15 hours
time taken by third pipe = (x –4) hours = 6 hours

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