One pipe fills a pool in 4 hours. A second pipe, used to drain the water from the pool, can empty the pool in 8 hours. The owner of the pool mistakenly opened both pipes. How long will it take to fill the pool if one pipe is filling and the other is emptying?

Question

misty1212 · Answer

Hi!!

calculusxy · Answer

Hi!

misty1212 · Answer

one has rate $\frac{1}{4}$ the other has rate $-\frac{1}{8}$ 
the combined rate is what you get when you ... combine them
what is $$\frac{1}{4}-\frac{1}{8}$$?

calculusxy · Answer

$\large \frac{2}{8} - \frac{1}{8} = \frac{1}{8}$

misty1212 · Answer

ok so the this system of silliness fills one eighths of the pool per hour

misty1212 · Answer

how many hours to fill the whole pool?

calculusxy · Answer

i don't understand but i guess $\large \frac{1}{8}$?

misty1212 · Answer

oh no

misty1212 · Answer

it fills only one eighths of the pool per hour

misty1212 · Answer

so how many hours for the entire pool to be filled?

calculusxy · Answer

okay

so do we divide $\large 1 \div \frac{1}{8}$ ?

misty1212 · Answer

you can, or i would just think
one eighths per hour, 8 hours for the whole pool

calculusxy · Answer

your thinking seems more logical. thank you!

misty1212 · Answer

$$\color\magenta\heartsuit$$