At 9 a.m., Mrs Pang used two taps to fill up a tank. Tap K could fill the tank in 5 h. Tap L could fill the tank in 4 h. 1 hour after both taps were turned on, Tap L was faulty and stopped working. Mrs Pang accidentally opened Tap M 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 K per hour
= ¹₅ tank

Rate of Tap L per hour
= ¹₄ tank

Rate of Tap M per hour
= ¹₃ tank

Fraction of the tank filled per hour by Tap K and Tap L
= ¹₅ + ¹₄
= ⁴₂₀ + ⁵₂₀
= ⁹₂₀

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

Time taken for the tank to be drained after first hour
= ⁹₂₀ ÷ ²₁₅
= ⁹₂₀ x ¹⁵₂
= 3³₈ h 

Total time taken for the tank to be empty
= 3³₈ + 1
= 4³₈ h

Answer(s): 4³₈ h