At 8 a.m., Mrs Choy used two taps to fill up a tank. Tap M could fill the tank in 6 h. Tap N could fill the tank in 4 h. 1 hour after both taps were turned on, Tap N was faulty and stopped working. Mrs Choy accidentally opened Tap P which could drain a full tank completely in 2 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 M per hour
= ¹₆ tank

Rate of Tap N per hour
= ¹₄ tank

Rate of Tap P per hour
= ¹₂ tank

Fraction of the tank filled per hour by Tap M and Tap N
= ¹₆ + ¹₄
= ⁴₁₂ + ⁶₁₂
= ¹⁰₁₂

Fraction of the tank drained per hour by Tap P when only Tap M is working
= ¹₂ - ¹₆
= ⁶₆ - ²₆
= ²₆

Time taken for the tank to be drained after first hour
= ¹⁰₁₂ ÷ ²₆
= ¹⁰₁₂ x ⁶₂
= 2¹₂ h 

Total time taken for the tank to be empty
= 2¹₂ + 1
= 3¹₂ h

Answer(s): 3¹₂ h