SOLUTION: Pump A can fill a tank in 6 hours. Pump B can empty the same tank in 10 hours. How long will it take both pumps working together to fill the tank?

Question 1163885: Pump A can fill a tank in 6 hours. Pump B can empty
the same tank in 10 hours. How long will it take both
pumps working together to fill the tank?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
A fills the tank in 6 hours
B empties the tank in 10 hours.

rate * time = quantity
time is in hours.
quantity is 1 tank
rate = quantity divided by time.

for pump A, the formula becomes rate * 6 = 1.
solve for rate to get pump A rate = 1/6 of the tank is filled each hour.

for pump B, the formula gecomew rate * 10 = 1.
solve for rate to get pump B rate = 1/10 of the tank is emptied each hour.

when one pump is working to fill the tank and one pump is working to empty the tank, their rates are subtractive.

if they were both working together to fill the tank, their rates would be additive.

the formula is therefore (rate A minus rate B) * time = 1
this formula becomes (1/6 minus 1/10) * time = 1
simplify to get (10/60 minus 6/60) * time = 1
combine like terms to get 4/60 * time = 1
solve for time to get time = 60/4 = 15 hours.

in 15 hours, pump A has filled 1/6 * 15 = 15/6 tanks.
in 15 hours, pump B has emptied 1/10 * 15 = 15/10 tanks.
15/6 minus 15/10 = 150/60 minus 90/60 = 60/60 = 1 tank.

RELATED QUESTIONS
Pump A can fill a tank in 10 hours. Pump B can empty the same tank in 15 hours. If both... (answered by ewatrrr)

Pump A can fill a tank in 15 hours, pump B can fill the same tank in 19 hours 20mins. If... (answered by ankor@dixie-net.com)

Pump A can fill a tank of water in 3 hours. Pump B can fill the same tank in 6 hours. How (answered by josgarithmetic,richwmiller)

Pump A can fill an empty 10,000 gallon tank in 4 hours, and auxiliary pump B can fill the (answered by ikleyn)

a pump can pump out water from a tank in 11 hours. another pump can pump out water from... (answered by nerdybill)

Pump R can fill a tank in 8 hours and Pump Q can empty it in 12 hours. If both pumps are (answered by ikleyn)

A pump can fill a tank in 6 hours. Another pump can fill the same tank in 3 hours. How... (answered by stanbon)

A tank can be filled in 18hours by "pump A" or in 24 hours by "pump B" how long will it... (answered by mananth)

two pumps working together can fill a tank in 2 hours. working alone the first pump can... (answered by fractalier)