Multiple choice

Pipe A is the filling pipe and Pipe B is an emptying pipe. If both are open, the pool fills in 10 hours. If the pool is full and pipe B is opened, the pool empties in 6.66 hrs. How long does it take the filling pipe to fill the empty pool?

  1. 4 hours

  2. 5 hours

  3. 4.5 hours

  4. 6 hours
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let A be the filling rate and B be the emptying rate. Given 1/A - 1/B = 1/10 and 1/B = 1/6.66 (which is 3/20). Substituting 1/B gives 1/A - 3/20 = 2/20, so 1/A = 5/20 = 1/4. Thus, pipe A takes 4 hours.

AI explanation

Let the fill rate of pipe A be 1/F and the empty rate of pipe B be 1/E. When both are open, they fill the pool in 10 hours, so 1/F minus 1/E equals 1/10. We are given that B empties the full pool in 6.66 hours, which is 20/3 hours, so the rate of B is 3/20. Substituting this into the first equation gives 1/F minus 3/20 equals 1/10. Solving for F gives 1/F equals 1/4, meaning it takes 4 hours for the filling pipe to fill the empty pool.

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