Two water taps together can fill a tank in 9 hrs 36 min . The tap of larger diameter takes 8 hr less than the smaller one to fill the tank separately.Find the time taken in which each tap can separately fill the tank.
Answers
Answered by
4
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.
Hope it helps you. Don't forget to mark the brainliest and rate 5 stars and also press the button "Thanks"
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.
Hope it helps you. Don't forget to mark the brainliest and rate 5 stars and also press the button "Thanks"
Answered by
3
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
Hope this helps
Mark it as
brainliest
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
Hope this helps
Mark it as
brainliest
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