Faucet N can fill a container completely in 3 hours while Faucet P takes 3 hours more to fill the same container completely. There is a hole at the bottom of the container which can empty the full container in 7 hours. How long does it take for the container to be completely filled if both faucets are turned on? Express your answer in mixed number of hours.
Time taken by only Faucet N to fill the container
= 3 h

3 h → 1 container
1 h → ¹₃ container

Time taken by only Faucet P  
= 3 + 3
= 6 h

6 h → 1 container
1 h → ¹₆ container

Time taken by only the hole to empty the container
= 7 h

7 h → 1 container
1 h → ¹₇ container

Time taken for the Faucet N, Faucet P and the hole to fill the container completely:
1 h → ¹₃ + ¹₆ - ¹₇ = ¹⁴₄₂ + ⁷₄₂ - ⁶₄₂ = ¹⁵₄₂ = ⁵₁₄ container

⁵₁₄ container → 1 h
1 container → 1 ÷ ⁵₁₄ = 1 x ¹⁴₅ = 2⁴₅ h

Time taken for the container to be completely filled = 2⁴₅ h

Answer(s): 2⁴₅ h