Paul uses two pipes to fill a pool. The first pipe can fill the pool in 3 h. The second pipe can fill the pool in 9 h. Two hours after both pipes are turned on, Vaidev 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 Paul to fill the pool completely. Express your answer in h.
Let the pool be 1 P.
The rate of the first pipe per hour= ¹₃
The rate of the second pipe per hour= ¹₉
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
= (¹₃ + ¹₉) x 2
= (⁶₁₈ + ²₁₈) x 2
= ⁸₁₈ x 2
= ¹⁶₁₈

Fraction of the remaining pool needed to be filled
= 1 - ¹⁶₁₈
= ²₁₈

Rate of filling up the pool per hour when 3rd pipe is open
= (1st pipe + 2nd pipe) - 3rd pipe
= ⁸₁₈ - ¹₆
= ⁸₁₈ - ³₁₈
= ⁵₁₈

Time taken to fill up the remaining pool
= ²₁₈ ÷ ⁵₁₈
= ²₁₈ x ¹⁸₅
= ³⁶₉₀ h

Time taken to fill the pool
= ³⁶₉₀ + 2
= 2.4 h

Answer(s): 2.4 h