At 10 a.m., Mrs Hun used two taps to fill up a tank. Tap S could fill the tank in 5 h. Tap T could fill the tank in 6 h. 1 hour after both taps were turned on, Tap T was faulty and stopped working. Mrs Hun accidentally opened Tap U 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 S per hour
= ¹₅ tank

Rate of Tap T per hour
= ¹₆ tank

Rate of Tap U per hour
= ¹₃ tank

Fraction of the tank filled per hour by Tap S and Tap T
= ¹₅ + ¹₆
= ⁶₃₀ + ⁵₃₀
= ¹¹₃₀

Fraction of the tank drained per hour by Tap U when only Tap S is working
= ¹₃ - ¹₅
= ⁵₁₅ - ³₁₅
= ²₁₅

Time taken for the tank to be drained after first hour
= ¹¹₃₀ ÷ ²₁₅
= ¹¹₃₀ x ¹⁵₂
= 2³₄ h 

Total time taken for the tank to be empty
= 2³₄ + 1
= 3³₄ h

Answer(s): 3³₄ h