Faucet K can fill a tank completely in 2 hours while Faucet L 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 6 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 K to fill the tank
= 2 h

2 h → 1 tank
1 h → ¹₂ tank

Time taken by only Faucet L  
= 2 + 3
= 5 h

5 h → 1 tank
1 h → ¹₅ tank

Time taken by only the hole to empty the tank
= 6 h

6 h → 1 tank
1 h → ¹₆ tank

Time taken for the Faucet K, Faucet L and the hole to fill the tank completely:
1 h → ¹₂ + ¹₅ - ¹₆ = ¹⁵₃₀ + ⁶₃₀ - ⁵₃₀ = ¹⁶₃₀ = ⁸₁₅ tank

⁸₁₅ tank → 1 h
1 tank → 1 ÷ ⁸₁₅ = 1 x ¹⁵₈ = 1⁷₈ h

Time taken for the tank to be completely filled = 1⁷₈ h

Answer(s): 1⁷₈ h