a tank can be filled by one pipe in 3.5 hours and emptied by another in 4.2 hours. if both pipes are running, how long will take to fill an empty tank ?
1 / 3.2 - 1 / 4.2 =
10 / 32 - 10 / 42 =
( 10 * 42 - 10 * 32 ) / ( 32 * 42 ) =
( 420 - 320 ) / 1344 = 100 / 1344 =
( 2 * 50 ) / ( 2 * 672 ) = 50 /672
1 / ( 50 / 672 ) = 672 / 50 =
13.44 h =
13 h 26 m 24 s
To find out how long it will take to fill an empty tank when both pipes are running, we need to calculate their combined rate of filling or emptying the tank.
Let's start by determining the rate at which each pipe fills or empties the tank:
- The first pipe fills the tank in 3.5 hours, which means it fills 1/3.5 (or 2/7) of the tank's capacity per hour.
- The second pipe empties the tank in 4.2 hours, so it empties 1/4.2 (or approximately 1/4.2) of the tank's capacity per hour.
Now, to calculate the combined rate of filling when both pipes are running, we subtract the rate of emptying from the rate of filling:
Rate of filling = 2/7 - 1/4.2
To simplify this expression, let's find a common denominator for both fractions. In this case, the least common multiple (LCM) of 7 and 4.2 is 14:
Rate of filling = (2/7)*(2/2) - (1/4.2)*(3.5/3.5)
= 4/14 - 3.5/14
= (4 - 3.5)/14
= 0.5/14
= 1/28
Now, we know that the filling rate when both pipes are running is 1/28 of the tank's capacity per hour.
To determine how long it will take to fill an empty tank, we need to divide the tank's capacity by the filling rate (1/28):
Time to fill = 1 / (1/28)
= 28/1
= 28 hours
Therefore, it will take 28 hours to fill an empty tank when both pipes are running.