a 7. A tap can fill a tank in 4 hours and another tap can fill it in 6 hours. Two outlet pipes can empty the tank in 8 hours and 12 hours respectively. All four were opened and allowed to run for 3 hours. Then the taps were closed. How long will the outlet pipes take to empty the tank?
Answers
Answer:
If we assume a sixty litre tank, then the math is easier.
4 hrs of in flow gives us a full 60L. thus the in-flow rate is 15 L/hr
6 hours of out flow to empty a full 60 L, gives us an out flow rate of 10 L/hr.
Both taps are open, 15 in per hour, 10 out per hour, overall flow rate is plus 5L per hour. 60L divided by 5 equals 12 hours.
It will take 12 hours to fill the tank.
To prove that this works for a tank of any size, takes a bit of algebra.
tank size of X litres. 4 hours to fill means a flow rate of 1/4X L/hr. 6 hours to empty means a flow rate of 1/6X L/hr. to find the difference in the flow and thus the remainder in the tank after any given hour, we subtract the flow rates.
1/4X minus 1/6X is the same as 3/12X minus 2/12X which is 1/12X L/hr. thus to get a full tank of X Litres, would require 12 hours.