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Question

It takes 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 smaller diameter is used for 9 hours, only half of the pool is filled. How long would each pipe take to fill the swimming pool ?


Solution

let the time taken by the 1 pipe be x hours and let the time taken by the 2 pipe be y hours.

& the in 1 hour the 1 pipe can fill it=1x

the in 1 hour the 2 pipe can fill it=1y

1x+1y=112           -1

4x+9y=12             -2

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

a+b=12           -3

4a + 9b = 12       -4

multiply 3 by 4 and then subtract 5 and 6.

4a +4b=13      -5

4a + 9b = 12     -6

we get, b=130

y=30.

sustituting the value of y in eq. 3

a+130 = 112

x=20.

Hence the 1 pipe would take 20hours and the 2 pipe would take 30 hours


Mathematics
Concise Mathematics
Standard IX

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