At 7 a.m., Mrs Yong used two taps to fill up a tank. Tap D could fill the tank in 7 h. Tap E could fill the tank in 4 h. 1 hour after both taps were turned on, Tap E was faulty and stopped working. Mrs Yong accidentally opened Tap F 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 D per hour
= ¹₇ tank

Rate of Tap E per hour
= ¹₄ tank

Rate of Tap F per hour
= ¹₂ tank

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

Fraction of the tank drained per hour by Tap F when only Tap D is working
= ¹₂ - ¹₇
= ⁷₁₄ - ²₁₄
= ⁵₁₄

Time taken for the tank to be drained after first hour
= ¹¹₂₈ ÷ ⁵₁₄
= ¹¹₂₈ x ¹⁴₅
= 1¹₁₀ h 

Total time taken for the tank to be empty
= 1¹₁₀ + 1
= 2¹₁₀ h

Answer(s): 2¹₁₀ h