Multiple choice

If two pipes are put in operation simultaneously, the tank is filled in $24$ min. One pipe fills the tank $20$ min faster than the other. How many hours does the faster pipe take to fill the tank ?

  1. $60$ min
  2. $45$ min
  3. $40$ min
  4. $30$ min
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the faster pipe take x minutes. The slower takes x+20. (1/x) + 1/(x+20) = 1/24. (2x+20)/(x(x+20)) = 1/24. 48x + 480 = x^2 + 20x. x^2 - 28x - 480 = 0. (x-40)(x+12) = 0. So x = 40 minutes.

AI explanation

Let the slower pipe take x minutes to fill the tank, so the faster pipe takes (x - 20) minutes. Using the sum of rates formula, 1/x + 1/(x - 20) = 1/24. Solving x^2 - 68x + 480 = 0 yields x = 60, meaning the faster pipe takes 60 - 20 = 40 minutes. The result is 40 min.

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