At 10 a.m., Mrs Loh used two taps to fill up a tank. Tap H could fill the tank in 7 h. Tap J could fill the tank in 6 h. 1 hour after both taps were turned on, Tap J was faulty and stopped working. Mrs Loh accidentally opened Tap K 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 H per hour
= ¹₇ tank

Rate of Tap J per hour
= ¹₆ tank

Rate of Tap K per hour
= ¹₃ tank

Fraction of the tank filled per hour by Tap H and Tap J
= ¹₇ + ¹₆
= ⁶₄₂ + ⁷₄₂
= ¹³₄₂

Fraction of the tank drained per hour by Tap K when only Tap H is working
= ¹₃ - ¹₇
= ⁷₂₁ - ³₂₁
= ⁴₂₁

Time taken for the tank to be drained after first hour
= ¹³₄₂ ÷ ⁴₂₁
= ¹³₄₂ x ²¹₄
= 1⁵₈ h 

Total time taken for the tank to be empty
= 1⁵₈ + 1
= 2⁵₈ h

Answer(s): 2⁵₈ h