At 10 a.m., Mrs Long used two taps to fill up a tank. Tap N could fill the tank in 8 h. Tap P could fill the tank in 5 h. 1 hour after both taps were turned on, Tap P was faulty and stopped working. Mrs Long accidentally opened Tap Q 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 N per hour
= ¹₈ tank

Rate of Tap P per hour
= ¹₅ tank

Rate of Tap Q per hour
= ¹₃ tank

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

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