Liam uses two pipes to fill a pool. The first pipe can fill the pool in 6 h. The second pipe can fill the pool in 9 h. Two hours after both pipes are turned on, Julian accidentally opens the pipe which can drain the pool completely in 10 h. With the 3rd pipe now remained open, what is the total time taken by Liam to fill the pool completely. Express your answer in h.
Let the pool be 1 P.
The rate of the first pipe per hour= ¹₆
The rate of the second pipe per hour= ¹₉
The rate of the third pipe per hour= ¹₁₀

Fraction of the pool filled by the 1st pipe and the 2nd pipe in two hours
= (¹₆ + ¹₉) x 2
= (¹⁵₉₀ + ¹⁰₉₀) x 2
= ²⁵₉₀ x 2
= ⁵⁰₉₀

Fraction of the remaining pool needed to be filled
= 1 - ⁵⁰₉₀
= ⁴⁰₉₀

Rate of filling up the pool per hour when 3rd pipe is open
= (1st pipe + 2nd pipe) - 3rd pipe
= ²⁵₉₀ - ¹₁₀
= ²⁵₉₀ - ⁹₉₀
= ¹⁶₉₀

Time taken to fill up the remaining pool
= ⁴⁰₉₀ ÷ ¹⁶₉₀
= ⁴⁰₉₀ x ⁹⁰₁₆
= 2⁷²⁰₁₄₄₀ h

Time taken to fill the pool
= 2⁷²⁰₁₄₄₀ + 2
= 4.5 h

Answer(s): 4.5 h