# Tub question

1. Sep 9, 2010

### Outblaze

1. Water is flowing from a faucet into an empty tub at 4.5 gallons/minute. After 4 minutes, a drain in the tub is opened, and the water begins to flow out at 6.3 gallons/minute.

a). Will the tub ever fill up completely without overflowing?

b). Will it ever empty completely?

c). What if the faucet is turned off after 4 minutes?

d). What if the rates of flow in and out are reversed?

e). What assumptions do we have to make in order to answer these questions?

2. Relevant equations

3. The way I thought of doing it was to take the 4.5 gallons that are flowing into the tub and subtract 6.3 gallons flowing out from it:

4.5 - 6.3 = -1.8
meaning that 1.8 gallons are lost per minute (not 6.3 because there's still water flowing from the tap into the tub).

Then I took the 18 gallons from the first 4 minutes and subtracted 1.8 gallons, giving me 20.7 gallons after the 5th minute. At the 16th minute, 0.9 gallons would be left in the tub (according to my equation). Thus the tub would not overflow because the rate at which the water is flowing out of the tub is less than the rate at which the water is going into the tub.

If the rates of flow in and out were reversed, the tub could overflow because the rate going in would be more than the rate going out.

6.3 - 4.5 = +1.8
meaning that 1.8 gallons are added per minute.

Does this make sense???