Multiple choice

Pipe $A$ can fill one fourth of a tank in $5$ hours and pipe $B$ can empty the full tank in $30$ hours.If both pipes are opened simultaneously, then in how many hours will the empty tank be filled.

  1. $10$
  2. $60$
  3. $25$
  4. $45$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Pipe A fills 1/4 of the tank in 5 hours, so it fills the whole tank in 20 hours. Its rate is 1/20 tank/hour. Pipe B empties the tank in 30 hours, so its rate is -1/30 tank/hour. Combined rate = 1/20 - 1/30 = (3-2)/60 = 1/60. The tank is filled in 60 hours.

AI explanation

First, find the total filling time for pipe A by multiplying the time it takes to fill one fourth of the tank by 4, which gives 20 hours. Using the LCM method, let the total capacity be 60 units, so pipe A fills at 3 units per hour and pipe B empties at 2 units per hour. When both are open, the net fill is 1 unit per hour, meaning it takes 60 hours to fill the 60-unit tank.

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