Question

two water taps together can fill a tank in 75/8 hrs.the larger tap takes 10 hrs less than the smaller tap to fill the tank separetely.find the time in which each tap can fil the tank separately

Answer 1

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.