At 10 a.m., Mrs Sim used two taps to fill up a tank. Tap T could fill the tank in 7 h. Tap U could fill the tank in 4 h. 1 hour after both taps were turned on, Tap U was faulty and stopped working. Mrs Sim 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
= ¹₇ tank

Rate of Tap U per hour
= ¹₄ tank

Rate of Tap V per hour
= ¹₂ tank

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

Fraction of the tank drained per hour by Tap V when only Tap T 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