At 11 a.m., Mrs Lau used two taps to fill up a tank. Tap G could fill the tank in 6 h. Tap H could fill the tank in 5 h. 1 hour after both taps were turned on, Tap H was faulty and stopped working. Mrs Lau accidentally opened Tap J 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 G per hour
= ¹₆ tank

Rate of Tap H per hour
= ¹₅ tank

Rate of Tap J per hour
= ¹₂ tank

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

Fraction of the tank drained per hour by Tap J when only Tap G is working
= ¹₂ - ¹₆
= ⁶₆ - ²₆
= ²₆

Time taken for the tank to be drained after first hour
= ¹¹₃₀ ÷ ²₆
= ¹¹₃₀ x ⁶₂
= 1¹₁₀ h 

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

Answer(s): 2¹₁₀ h