A pipe fills an empty reservoir in 6 hours, while a drainage pipe empties it in 10 hours. If both pipes are opened simultaneously, how long does it take to fill the reservoir?
Answer and explanation
Correct answer: D. 15 hours
- Step 1: Calculate individual hourly rates: Fill rate = 1/6, Drain rate = 1/10.
- Step 2: Compute net filling rate per hour: 1/6 - 1/10 = 5/30 - 3/30 = 2/30 = 1/15.
- Step 3: Take the reciprocal of the net rate: 1 / (1/15) = 15 hours.
Answer
15 hours.
Why not the others: Option 12 hours averages 6 and 10 or adds times incorrectly. Option 8 hours subtracts the hours directly (10 - 6 = 4 or (10+6)/2). Option 16 hours adds 6 and 10.
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