Multiple choice

A tank has 3 pipes. The first pipe can fill $\displaystyle\frac { 1 }{ 2 }$ part of the tank in 1 hour and the second pipe can fill $\displaystyle\frac { 1 }{ 3 }$ part in 1 hour. The third pipe is for making the tank empty. When all the three pipes are open, $\displaystyle\frac { 7 }{ 12 }$ part of the tank is filled in 1 hour. How much time will the third pipe take to empty the completely filled tank?

  1. $3$ hours
  2. $4$ hours
  3. $5$ hours
  4. $6$ hours
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The first pipe fills 1/2 per hour, the second 1/3 per hour. Together they fill 1/2 + 1/3 = 5/6 per hour. With the third pipe (C) open, the net rate is 7/12. Thus, 5/6 - C = 7/12. Solving for C gives 10/12 - 7/12 = 3/12 = 1/4. The third pipe empties 1/4 of the tank per hour, so it takes 4 hours to empty the full tank.

AI explanation

We use the net work equation where the part of the tank filled in one hour equals the sum of the individual filling rates minus the emptying rate. The first pipe fills half the tank in one hour, the second fills a third in one hour, and together with the third pipe they fill 7/12 of the tank in one hour, establishing the equation 1/2 + 1/3 - 1/x = 7/12. Adding the filling rates gives 5/6, so the equation becomes 5/6 - 7/12 = 1/x, which simplifies to 3/12, meaning the third pipe empties 1/4 of the tank in one hour. Therefore, the third pipe takes 4 hours to empty the completely filled tank.

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