At 11 a.m., Mrs Chan used two taps to fill up a tank. Tap T could fill the tank in 8 h. Tap U could fill the tank in 6 h. 1 hour after both taps were turned on, Tap U was faulty and stopped working. Mrs Chan accidentally opened Tap V 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 T per hour
= ¹₈ tank

Rate of Tap U per hour
= ¹₆ tank

Rate of Tap V per hour
= ¹₂ tank

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

Fraction of the tank drained per hour by Tap V when only Tap T is working
= ¹₂ - ¹₈
= ⁸₈ - ²₈
= ³₈

Time taken for the tank to be drained after first hour
= ¹⁴₂₄ ÷ ³₈
= ¹⁴₂₄ x ⁸₃
= 1⁵₉ h 

Total time taken for the tank to be empty
= 1⁵₉ + 1
= 2⁵₉ h

Answer(s): 2⁵₉ h