SOLUTION: one pipe can fill a pool in 6 hours. The drain can empty the whole pool in 12 hours. With the pipe and the drain open how long will it take the pool to be filled? Mr.Poly Nomi

Algebra ->  Rate-of-work-word-problems -> SOLUTION: one pipe can fill a pool in 6 hours. The drain can empty the whole pool in 12 hours. With the pipe and the drain open how long will it take the pool to be filled? Mr.Poly Nomi      Log On


   

Question 938665: one pipe can fill a pool in 6 hours. The drain can empty the whole pool in 12 hours. With the pipe and the drain open how long will it take the pool to be filled?

Mr.Poly Nomials takes 8 hours to paint his room. After working for one hour , he called in a painter to help him. Working together they finished the job 3 more hours. How long would it take the painter to finish the job if he had worked alone?
Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!
one pipe can fill a pool in 6 hours. The drain can empty the whole pool in 12 hours. With the pipe and the drain open how long will it take the pool to be filled?
(1)
Let x=time it takes to fill pool with both pipes open
with both pipes open they fill at the rate of 1/x of the pool per hour
Fill pipe fills at the rate of 1/6 of the pool per hour
Drain pipe empties at the rate of 1/12 of the pool per hour
So, our equation to solve is:
(1/6)-(1/12)=(1/x) multiply each term by 12x
2x-x=12
x=12 hours
CK
In 12 hours, fill pipe fills (1/6)*12=2 pools
In 12 hours, drain pipe drains (1/12)*12=1 pool
So in twelve hours we have a net total of 1 pool filled:)
Mr.Poly Nomials takes 8 hours to paint his room. After working for one hour , he called in a painter to help him. Working together they finished the job 3 more hours. How long would it take the painter to finish the job if he had worked alone?
(2)
Let x=amount of time it takes painter to paint the room
And let t=time it takes painter to finish the room working alone
So painter works at the rate of 1/x of the room per hour
Poly works at the rate of 1/8 of the room per hour
So after 1 hour poly paints 1/8 of the room, leaving 7/8 of the room yet to be painted
So:
(1/8)*3+(1/x)*3=7/8
3/8 +3/x=7/8 multiply each term by 8x
3x+24=7x
4x=24
x=6 hours amount of time it takes painter working alone to paint the whole room
Now we know the painter paints at the rate of (1/6) room per hour
Now our problem to solve is:
(1/6)*t=7/8 multiply each term by 24
4t=21
t=21/4 =5 1/4 hours----Time it takes painter to finish the job working alone.
Does this help?---ptaylor