Two water taps together can fill a tank in 6 hours. The tap of larger diameter takes 9 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.

Answer

9 hours, 18 hours

Explanation

Let the faster tap take x hours to fill the tank.
Then, the slower tap takes `(x+9)` hours to fill it.
`:." "(1)/(x)+(1)/((x+9))=(1)/(6)implies6(2x+9)=x(x+9)`
`implies" "x^(2)-3x-54=0impliesx^(2)-9x+6x-54=0.`