Two water taps together can fill a tank in 9.38 hours. The tap of larger diameter takes 10 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank
Answers
Answer:
small one is take 38.76
and the big one take 28.76
Answer:
the tap with smaller diameter fills the tank alone in 25 hours where as the larger diameter fills the tank alone in 15 hours.
Step-by-step explanation:
tap with smaller diameter take x hours.
tap with larger diameter take (x – 10) hours.
In 1 hour, the tap with smaller diameter can fill 1/x part of the tank.
In 1 hour, the tap with larger diameter can fill 1/(x – 10) part of the tank.
The tank is filled up in 75/8 hours.
Thus, 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.
Thus, the tap with smaller diameter fills the tank alone in 25 hours where as the larger diameter fills the tank alone in 15 hours.