Multiple choice

A water tank is two-fifth full. Pipe A can fill the tank in 10 minutes and pipe B can empty it in 6 minutes. If both the pipes are opened, how long will it take to empty or fill the tank completely?

  1. 6 minutes to empty

  2. 9 minutes to fill

  3. 9 minutes to empty

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Tank is 2/5 full. Pipe A fills at 1/10 per min, Pipe B empties at 1/6 per min. Net rate = 1/10 - 1/6 = (3-5)/30 = -2/30 = -1/15 per min. To empty 2/5 of the tank: (2/5) / (1/15) = (2/5) * 15 = 6 minutes.

AI explanation

The tank is 2/5 full initially, meaning 2/5 of the tank must be emptied. The net rate of emptying when both pipes are open is 1/6 minus 1/10 per minute. Finding a common denominator of 30 gives a net rate of 5/30 minus 3/30, which equals 2/30 or 1/15 per minute. The time to empty 2/5 of the tank is the amount of water divided by the net rate, so (2/5) divided by (1/15) equals 6 minutes to empty.

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