Pipe L can fill a pool in 30 hours and pipe M in 45 hours. If both the pipes are opened in an empty pool, how much time will they take to fill it together?

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Let the capacity of the pool be 1 unit.

Pipe L fills the pool in 30 hours, so its rate = 1/30 per hour.
Pipe M fills the pool in 45 hours, so its rate = 1/45 per hour.

Combined rate = (1/30) + (1/45)
To add, take LCM of 30 and 45, which is 90.
(1/30) = 3/90
(1/45) = 2/90
So, combined rate = (3/90) + (2/90) = 5/90 = 1/18 per hour.

Time taken to fill the pool = 1 / (1/18) = 18 hours.

Therefore, both pipes together will fill the pool in 18 hours.

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