At 11 a.m., Mrs Song used two taps to fill up a tank. Tap F could fill the tank in 5 h. Tap G could fill the tank in 4 h. 1 hour after both taps were turned on, Tap G was faulty and stopped working. Mrs Song accidentally opened Tap H which could drain a full tank completely in 2 h. Instead of being filled, the tank was emptied. How long did it take for the tank to be completely empty? Express your answer in mixed number.
Rate of Tap F per hour
= ¹₅ tank

Rate of Tap G per hour
= ¹₄ tank

Rate of Tap H per hour
= ¹₂ tank

Fraction of the tank filled per hour by Tap F and Tap G
= ¹₅ + ¹₄
= ⁴₂₀ + ⁵₂₀
= ⁹₂₀

Fraction of the tank drained per hour by Tap H when only Tap F is working
= ¹₂ - ¹₅
= ⁵₁₀ - ²₁₀
= ³₁₀

Time taken for the tank to be drained after first hour
= ⁹₂₀ ÷ ³₁₀
= ⁹₂₀ x ¹⁰₃
= 1¹₂ h 

Total time taken for the tank to be empty
= 1¹₂ + 1
= 2¹₂ h

Answer(s): 2¹₂ h