Two water taps together can fill a tank in 9 hours 36mintes. The tap of larger diameter takes 8hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.
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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.
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.
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