At 10 a.m., Mrs Leng used two taps to fill up a tank. Tap D could fill the tank in 8 h. Tap E could fill the tank in 6 h. 1 hour after both taps were turned on, Tap E was faulty and stopped working. Mrs Leng accidentally opened Tap F 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 D per hour
= ¹₈ tank

Rate of Tap E per hour
= ¹₆ tank

Rate of Tap F per hour
= ¹₃ tank

Fraction of the tank filled per hour by Tap D and Tap E
= ¹₈ + ¹₆
= ⁶₂₄ + ⁸₂₄
= ¹⁴₂₄

Fraction of the tank drained per hour by Tap F when only Tap D is working
= ¹₃ - ¹₈
= ⁸₂₄ - ³₂₄
= ⁵₂₄

Time taken for the tank to be drained after first hour
= ¹⁴₂₄ ÷ ⁵₂₄
= ¹⁴₂₄ x ²⁴₅
= 2⁴₅ h 

Total time taken for the tank to be empty
= 2⁴₅ + 1
= 3⁴₅ h

Answer(s): 3⁴₅ h