Pipe A fills an empty tank in 6 hours and pipe B fills it in 9 hours, while drain C empties a full tank in 18 hours. If all three are open together, how long does the empty tank take to fill?

Answer and explanation

Correct answer: D. 4.5 hours

  1. Step 1: Write each rate as a fraction of the tank per hour: A = 1/6, B = 1/9, drain C = -1/18.
  2. Step 2: Add the rates over the common denominator 18: 3/18 + 2/18 - 1/18 = 4/18 = 2/9 of the tank per hour.
  3. Step 3: Time = 1 / (2/9) = 9/2 = 4.5 hours.
Answer
4.5 hours.
Why not the others: 3.6 hours is the time when the drain is ignored (1/6 + 1/9 = 5/18); 5.0 hours and 4.0 hours come from rounding or subtracting the drain time incorrectly.

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