Question

two water taps together can fill a tank in 9 hour to 36 minutes the tap of the larger diameter takes 8 hours less than the smaller one to fill the tank separately find the time in which each type can separately fill the tank

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 timeBut x = 25 then x – 10 = 15

Answer 2

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