At 11 a.m., Mrs Peh used two taps to fill up a tank. Tap U could fill the tank in 8 h. Tap V could fill the tank in 5 h. 1 hour after both taps were turned on, Tap V was faulty and stopped working. Mrs Peh accidentally opened Tap W 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 U per hour
= ¹₈ tank

Rate of Tap V per hour
= ¹₅ tank

Rate of Tap W per hour
= ¹₃ tank

Fraction of the tank filled per hour by Tap U and Tap V
= ¹₈ + ¹₅
= ⁵₄₀ + ⁸₄₀
= ¹³₄₀

Fraction of the tank drained per hour by Tap W when only Tap U is working
= ¹₃ - ¹₈
= ⁸₂₄ - ³₂₄
= ⁵₂₄

Time taken for the tank to be drained after first hour
= ¹³₄₀ ÷ ⁵₂₄
= ¹³₄₀ x ²⁴₅
= 1¹⁴₂₅ h 

Total time taken for the tank to be empty
= 1¹⁴₂₅ + 1
= 2¹⁴₂₅ h

Answer(s): 2¹⁴₂₅ h