two pump can individual fill the tank in 10 hours and 12 hours respectively while a third pump empites the full tank in 20 hours.If all the three pump are run simultaneously,in how munch time will be the tank be filled?
1/x = 1/10 + 1/12 - 1/20
x = 15/2
12/120 + 10/120 - 6/120
16/120 = 1/x
120/16 = x
15/2 =x
To find out how much time it will take to fill the tank when all three pumps are run simultaneously, we need to calculate the combined rate at which the pumps fill and empty the tank.
Let's first find the rate at which each pump fills or empties the tank per hour:
Pump 1: Fills 1 tank in 10 hours -> Fills 1/10 of a tank per hour
Pump 2: Fills 1 tank in 12 hours -> Fills 1/12 of a tank per hour
Pump 3: Empties 1 tank in 20 hours -> Empties 1/20 of a tank per hour
Now, let's calculate the combined rate at which the pumps work when run simultaneously. Since Pump 3 empties the tank, we'll subtract its rate from the combined filling rate:
Combined filling rate = (1/10) + (1/12) - (1/20)
= (12/120) + (10/120) - (6/120)
= 16/120
= 2/15
Therefore, when all three pumps are run simultaneously, they fill the tank at a rate of 2/15 of a tank per hour.
To find out how much time it will take to fill the tank, we can use the formula:
Time = Amount / Rate
Let's denote the time required to fill the tank as T:
T = 1 (since we want to fill the entire tank)
Rate = 2/15
T = 1 / (2/15)
T = 15/2
T = 7.5
Therefore, it will take 7.5 hours (or 7 hours and 30 minutes) to fill the tank when all three pumps are run simultaneously.