SOLUTION: Please help me to solve this probblem: A tank can be filled by one pipe in 5 hours and by another pipe in 8 hours. It can be emptied by a drain pipe in 6 hours. If all three pipes

Question 958151: Please help me to solve this probblem: A tank can be filled by one pipe in 5 hours and by another pipe in 8 hours. It can be emptied by a drain pipe in 6 hours. If all three pipes are open, how long will it take to fill the tank?
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
Let x=amount of time it takes to fill the tank with all three pipes open
All three pipes fill at the rate of 1/x of the tank per hour
One pipe fills at the rate of 1/5 of the tank per hour
Another pipe fills at the rate of 1/8 tank per hour
Drain pipe drains at the rate of 1/6 tank per hour
Sooooo
1/5 + 1/8 - 1/6= 1/x multiply each term by 120x
24x+15x-20x=120
19x=120
x=6.32 hours
CK
We'll deal in fractions to eliminate round-off errors
In (120/19) hours one pipe fills (120/19)(1/5)=24/19 tank
In (120/19) hours another pipe fills (120/19)(1/8)=15/19 tank
In (120/19) hours drain pipe drains (120/19)(1/6)=20/19 tank
Soooo 24/19 + 15/19 - 20/19 should equal 1 tank and it does

Hope this helps----ptaylor

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