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 ?

Answer 1

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=$\frac{1}{x}$

the in 1 hour the 2 pipe can fill it=$\frac{1}{y}$

$\frac{1}{x}+\frac{1}{y}=\frac{1}{12}$ -1

$\frac{4}{x}+\frac{9}{y}=\frac{1}{2}$ -2

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

a+b=$\frac{1}{2}$ -3

4a + 9b = $\frac{1}{2}$ -4

multiply 3 by 4 and then subtract 5 and 6.

4a +4b=$\frac{1}{3}$ -5

4a + 9b = $\frac{1}{2}$ -6

we get, b=$\frac{1}{30}$

y=30.

sustituting the value of y in eq. 3

a+$\frac{1}{30}$ = $\frac{1}{12}$

x=20.

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