Simon uses two pipes to fill a pool. The first pipe can fill the pool in 4 h. The second pipe can fill the pool in 8 h. Two hours after both pipes are turned on, Rael accidentally opens the pipe which can drain the pool completely in 6 h. With the 3rd pipe now remained open, what is the total time taken by Simon to fill the pool completely. Express your answer in h.
Let the pool be 1 P.
The rate of the first pipe per hour= ¹₄
The rate of the second pipe per hour= ¹₈
The rate of the third pipe per hour= ¹₆

Fraction of the pool filled by the 1st pipe and the 2nd pipe in two hours
= (¹₄ + ¹₈) x 2
= (⁶₂₄ + ³₂₄) x 2
= ⁹₂₄ x 2
= ¹⁸₂₄

Fraction of the remaining pool needed to be filled
= 1 - ¹⁸₂₄
= ⁶₂₄

Rate of filling up the pool per hour when 3rd pipe is open
= (1st pipe + 2nd pipe) - 3rd pipe
= ⁹₂₄ - ¹₆
= ⁹₂₄ - ⁴₂₄
= ⁵₂₄

Time taken to fill up the remaining pool
= ⁶₂₄ ÷ ⁵₂₄
= ⁶₂₄ x ²⁴₅
= 1²⁴₁₂₀ h

Time taken to fill the pool
= 1²⁴₁₂₀ + 2
= 3.2 h

Answer(s): 3.2 h