Faucet A can fill a tank completely in 3 hours while Faucet B takes 3 hours more to fill the same tank completely. There is a hole at the bottom of the tank which can empty the full tank in 10 hours. How long does it take for the tank to be completely filled if both faucets are turned on? Express your answer in mixed number of hours.
Time taken by only Faucet A to fill the tank
= 3 h

3 h → 1 tank
1 h → ¹₃ tank

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

6 h → 1 tank
1 h → ¹₆ tank

Time taken by only the hole to empty the tank
= 10 h

10 h → 1 tank
1 h → ¹₁₀ tank

Time taken for the Faucet A, Faucet B and the hole to fill the tank completely:
1 h → ¹₃ + ¹₆ - ¹₁₀ = ¹⁰₃₀ + ⁵₃₀ - ³₃₀ = ¹²₃₀ = ²₅ tank

²₅ tank → 1 h
1 tank → 1 ÷ ²₅ = 1 x ⁵₂ = 2¹₂ h

Time taken for the tank to be completely filled = 2¹₂ h

Answer(s): 2¹₂ h