At 6 a.m., Mrs Lau used two taps to fill up a tank. Tap F could fill the tank in 7 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 Lau accidentally opened Tap H which could drain a full tank completely in 3 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
= ¹₇ tank

Rate of Tap G per hour
= ¹₄ tank

Rate of Tap H per hour
= ¹₃ tank

Fraction of the tank filled per hour by Tap F and Tap G
= ¹₇ + ¹₄
= ⁴₂₈ + ⁷₂₈
= ¹¹₂₈

Fraction of the tank drained per hour by Tap H when only Tap F is working
= ¹₃ - ¹₇
= ⁷₂₁ - ³₂₁
= ⁴₂₁

Time taken for the tank to be drained after first hour
= ¹¹₂₈ ÷ ⁴₂₁
= ¹¹₂₈ x ²¹₄
= 2¹₁₆ h 

Total time taken for the tank to be empty
= 2¹₁₆ + 1
= 3¹₁₆ h

Answer(s): 3¹₁₆ h