Multiple choice

In a town, three water pipes with circular cross-sections are being installed. The diameters of these pipes are 5 cm, 7 cm, and 9 cm. When all three pipes are opened simultaneously, they can fill a reservoir in 3 hours. Due to maintenance, if only the first two pipes, with diameters of 5 cm and 7 cm are used, how long will it take to fill the reservoir under these conditions?

  1. 2 hours and 15 minutes

  2. 6 hours and 17 minutes

  3. 6 hours and 27 minutes

  4. 6 hours and 47 minutes
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Flow rate is proportional to the cross-sectional area (diameter squared). Rates are 25k, 49k, 81k. Total rate = 155k. Reservoir = 155k * 3 = 465k. Using only 5cm and 7cm pipes: Rate = 25k + 49k = 74k. Time = 465k / 74k = 6.2837 hours. 0.2837 * 60 = 17.02 minutes. So 6 hours and 17 minutes.

AI explanation

The filling rates of pipes with circular cross-sections are proportional to the square of their diameters. The ratios of the rates for the three pipes are 5 squared, 7 squared, and 9 squared, which is 25, 49, and 81. The sum of these ratios is 155, and since all three together fill the reservoir in 3 hours, their combined rate is 155 units every 3 hours. The rate for the first two pipes is 25 plus 49, totaling 74 units every 3 hours, meaning their combined rate is 24.67 units per hour. Dividing the total capacity of 155 units by 24.67 gives approximately 6.28 hours, which is 6 hours and 17 minutes.

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