At 9 a.m., Mrs Lau used two taps to fill up a tank. Tap Z could fill the tank in 7 h. Tap A could fill the tank in 5 h. 1 hour after both taps were turned on, Tap A was faulty and stopped working. Mrs Lau accidentally opened Tap B 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 Z per hour
= ¹₇ tank

Rate of Tap A per hour
= ¹₅ tank

Rate of Tap B per hour
= ¹₃ tank

Fraction of the tank filled per hour by Tap Z and Tap A
= ¹₇ + ¹₅
= ⁵₃₅ + ⁷₃₅
= ¹²₃₅

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

Time taken for the tank to be drained after first hour
= ¹²₃₅ ÷ ⁴₂₁
= ¹²₃₅ x ²¹₄
= 1⁴₅ h 

Total time taken for the tank to be empty
= 1⁴₅ + 1
= 2⁴₅ h

Answer(s): 2⁴₅ h