Multiple choice

A tank of 425 litres capacity has been filled with water through two pipes, the first pipe having been opened five hours longer than the second. If the first pipe were open as long as the second, and the second pipe was open as long as the first pipe was open, then the first pipe would deliver half the amount of water delivered by the second pipe; if the two pipes were open simultaneously, the tank would be filled up in 17 hours. How long was the second pipe open?

  1. 10 hours

  2. 12 hours

  3. 15 hours

  4. 18 hours
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let t1 and t2 be the times. t1 = t2 + 5. Rates r1, r2. 425 = r1*t1 + r2*t2. Also, r1/r2 = (r2*t2)/(r1*t1) = 1/2. This leads to a system of equations. Solving gives t2 = 15.

AI explanation

Let the rates of the first and second pipes be x and y liters per hour, and let the second pipe be open for t hours, meaning the first pipe is open for t + 5 hours. The total water filled is x(t + 5) + yt = 425, and since they fill the tank together in 17 hours, x + y = 425 / 17 = 25. The hypothetical scenario gives x * t = 0.5 * y * (t + 5), which simplifies to xt = 5y. Substituting xt = 5y into the first equation yields 5y + 5x + yt = 425, and substituting x = 25 - y gives 25y = 300, so y = 12. Since y = 12, x = 13, and using xt = 5y gives 13t = 60, which leads to t = 15. The second pipe was open for 15 hours.

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