SOLUTION: An inlet pipe can fill a tank in 6 hours and another inlet pipe can fill it in 8 hours while an outlet pipe can drain it in 12 hours. If all pipes are open at the same time, how l

Algebra ->  Rate-of-work-word-problems -> SOLUTION: An inlet pipe can fill a tank in 6 hours and another inlet pipe can fill it in 8 hours while an outlet pipe can drain it in 12 hours. If all pipes are open at the same time, how l      Log On


   

Question 997214: An inlet pipe can fill a tank in 6 hours and another inlet pipe can fill it in 8 hours while an outlet pipe can drain it in 12 hours. If all pipes are open at the same time, how long will it take to fill an empty tank?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
PIPE          RATE in TANK per HOUR
inlet1         1/6
inlet2         1/8
outlet        -1/12

Combined rate for all pipes together is 1%2F6%2B1%2F8-1%2F12, and some arithmetic makes this
%281%2F6%29%284%2F4%29%2B%281%2F8%29%283%2F3%29-%281%2F12%29%282%2F2%29
4%2F24%2B3%2F24-2%2F24
%287-2%29%2F24
highlight%285%2F24%29-----POSITIVE VALUE, here meaning that the combined pipes opened will FILL the tank. They will not empty the tank!

These three combined pipes will FILL an empty tank in 24%2F5=4%264%2F5 hours.