At 7 a.m., Mrs Yee used two taps to fill up a tank. Tap Q could fill the tank in 5 h. Tap R could fill the tank in 4 h. 1 hour after both taps were turned on, Tap R was faulty and stopped working. Mrs Yee accidentally opened Tap S 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 Q per hour
= ¹₅ tank

Rate of Tap R per hour
= ¹₄ tank

Rate of Tap S per hour
= ¹₃ tank

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

Fraction of the tank drained per hour by Tap S when only Tap Q 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