Multiple choice

Two pipes can fill an empty tank separately in $24$ minutes and $40$ minutes respectively and a third pipe can empty $30$ gallons of water per minute. If all the three pipes are open, empty tanks becomes full in one hour. The capacity of tank (in gallons) is

  1. $500$
  2. $550$
  3. $600$
  4. $700$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let C be the capacity. The rates of the three pipes are C/24, C/40, and -30. Combined, they fill the tank in 60 minutes: C/24 + C/40 - 30 = C/60. Solving for C: C(1/24 + 1/40 - 1/60) = 30, which simplifies to C(5/120 + 3/120 - 2/120) = 30, or C(6/120) = 30, so C = 600.

AI explanation

Using the capacity method, assume the total capacity of the tank is the least common multiple of 24, 40, and 60, which is 120 gallons. The filling rates of the first two pipes are 5 gallons per minute and 3 gallons per minute. Since the tank fills in one hour with all pipes open, the net filling rate is 120 gallons per 60 minutes, or 2 gallons per minute. Setting up the equation 5 + 3 - Rate of third pipe = 2 shows the third pipe empties at 6 gallons per minute. Given the third pipe empties 30 gallons per minute, the actual tank capacity is scaled up by a factor of 5, making it 600 gallons.

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