Question

The cold water faucet of a bathtub can fill the tub in 15 minutes. The drain, when opened, can empty the full tub in 20 minutes. Suppose the tub is empty and the faucet and drain are both opened at the same time. How long will it take to fill the tub?

Answer 1

10 minutes

Explanation:

This is because if u have both the faucet and drain on at the same time, it will fill the tub faster

Answer 2

60 minutes

Explanation:

• faucet takes 15 minutes to fill the tub, so how much of the full tub is added per minute?
• 
  `15 minutes=1added/minute\\1minute=(1)/(15) added/minute`
• drain takes 20 minutes to empty the tub so how much of the full tub is lost per minute?
• 
  `20minutes=1lost/minute\\1minute=(1)/(20) lost/minute`
• How long it takes to fill the tub can be found by how much of it is added per minute minus lost per minute
• 
  `totalfilled/minute=added/minute-lost/minute\\=(1)/(15) -(1)/(20)=(1)/(60)`
• So one sixtieth of the tub is filled a minute, so that 60 parts of the tub, each taking a minute, that's 60 minutes or 1 hour