Asoda bottle can be filled completely by a faucet in 10 seconds. the bottle also has a hole that can drain the full soda bottle to empty in 30 seconds. if the bottle is initially empty when the faucet is turned on, how long will it take for the bottle to be fully filled?

The faucet can fill the bottle in 10 seconds ... it fills 1/10 of the bottle each second.

The hole drains the bottle in 30 seconds ... it drains 1/30 of the bottle in 1 second.

If the faucet and the hole are both working at the same time, then the bottle is filling at the rate of  (1/10 of a bottle) - (1/30 of a bottle) each second.

That number is (1/10 - 1/30) = (3/30 - 1/30) = (2/30) = 1/15 bottle per second.

The bottle is filling at the rate of 1/15 bottle per second.

So it'll be filled to the rim of the brim in 15 seconds.

3.2x10^7