if pump A can empty a tank in 2 hours and pump B can empty the tank in 4 hours ,how long will they take to empty the tank if they run together
A = (1 / 2 ) tank/hr
B = (1 / 4) tank/hr
A + B =1/'2 + 1/4 = 3/4 tank /hr
t hr (3 tank / 4 hr) = 1 tank
t = 4/3 hr
To find out how long it will take for pumps A and B to empty the tank when they operate together, we need to calculate their combined rate of emptying.
Let's start by determining the individual rates of each pump:
- Pump A can empty the tank in 2 hours, so its rate is 1/2 of the tank per hour. (1 tank / 2 hours = 1/2 tank per hour)
- Pump B can empty the tank in 4 hours, so its rate is 1/4 of the tank per hour. (1 tank / 4 hours = 1/4 tank per hour)
Now, to find their combined rate, we add the rates of pumps A and B:
Combined rate = Pump A's rate + Pump B's rate
Combined rate = 1/2 tank per hour + 1/4 tank per hour
Combined rate = 2/4 tank per hour + 1/4 tank per hour
Combined rate = 3/4 tank per hour
Therefore, when pumps A and B are operated together, they will empty the tank at a combined rate of 3/4 of the tank per hour.
To calculate the time it will take to empty the tank, we can use the formula:
Time = Quantity / Rate
In this case, the quantity is 1 tank and the rate is 3/4 tank per hour.
Time = 1 tank / (3/4 tank per hour)
To divide by a fraction, we invert the fraction and multiply:
Time = 1 tank * (4/3 tank per hour)
Time = 4/3 hour
So, it will take pumps A and B 4/3 or approximately 1.33 hours to empty the tank when they run together.
To find out how long it will take for pumps A and B to empty the tank when running together, you can use the concept of work rates.
The work rate of a pump is the amount of work it can do in a given time. In this case, the work rate is the amount of tank emptied per hour.
Pump A can empty the tank in 2 hours, so its work rate is 1/2 (1 tank / 2 hours = 1/2 tank per hour).
Pump B can empty the tank in 4 hours, so its work rate is 1/4 (1 tank / 4 hours = 1/4 tank per hour).
When the pumps are working together, their work rates are combined. Therefore, their combined work rate is the sum of their individual work rates, which is 1/2 + 1/4 = 3/4 tank per hour.
To calculate how long it will take for the pumps to empty the tank when working together, you can divide the total work (1 tank) by the combined work rate (3/4 tank per hour):
Time = Total Work / Combined Work Rate
Time = 1 tank / (3/4 tank per hour)
Time = 4/3 hours
Therefore, it will take pumps A and B to empty the tank approximately 1 hour and 20 minutes when running together.