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 ?
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
let 1/x be a and 1/y be b.
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
sustituting the value of y in eq. 3
a+130 = 112
Hence the 1 pipe would take 20hours and the 2 pipe would take 30 hours