EXAMPLE 7 Two water taps together can fill a tank in 75/8hours. The larger takes 10 hours less
than the smaller one to fill the tank separately. Formulate the quadratic equation to find the time in
which each tap can separately fill the tank.
Answers
Sol : Let the tap of the larger diameter fills the tank alone in (x – 10) hours. In 1 hour, the tap of the smaller diameter can fill 1/x part of the tank. In 1 hour, the tap of the larger diameter can fill 1/(x – 10) part of the tank. Two water taps together can fii a tank in 75 / 8 hours. But in 1 hour the taps fill 8/75 part of the tank. 1 / x + 1 / (x – 10) = 8 / 75. ( x – 10 + x ) / x ( x – 10) = 8 / 75. 2( x – 5) / ( x2 – 10 x) = 8 / 75. 4x2 – 40x = 75x – 375. 4x2 – 115x + 375 = 0 4x2 – 100x – 15x + 375 = 0 4x ( x – 25) – 15( x – 25) = 0 ( 4x -15)( x – 25) = 0. x = 25, 15/ 4. But x = 15 / 4 then x – 10 = -25 /4 which is not possible since time But x = 25 then x – 10 = 15. Larger diameter of the tap can the tank 15 hours and smaller diameter of the tank can fill the tank in 25 hours.