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Question

It take 12 hours to fill a swimming pool using two pipes. If the pipe of larger diameter is used for 4 hours and the pipe of smallerdiameterbfor 9 hours only half the pool can be filled .How long would it take for each pipe tobfill the pool separately


Solution

let the time taken by the first pipe be x hours and the time taken by the second pipe be y hours.

 in 1 hour the first pipe can fill it = 1/x

 in 1 hour the second pipe can fill it = 1/y

1/x +1/y = 1/12 --------------(1)

4/x +9/y =1/2---------------(2)

Consider 1/x be a and 1/y be b.

a + b = 1/12 -------------(3)

4a + 9b = 1/2 ----------------(4)

multiply (3)×4

4a + 4b =1/3 --------------(5)

(4)-(5) gives 5b=1/6

we get, b = 1/30

y = 30.

sustituting the value of y in equ(3) we get

a + 1/30 = 1/12

x = 20.

Hence the first pipe would take 20hours and the second pipe would take 30 hours.


Mathematics

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