Problem 6 · 2009 AMC 8
Easy
Ratios, Rates & Proportions
combined-rate
Steve's empty swimming pool will hold 24,000 gallons of water when full. It will be filled by 4 hoses, each of which supplies 2.5 gallons of water per minute. How many hours will it take to fill Steve's pool?
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Answer: A — 40 hours.
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Hint 1 of 2
Four hoses running at once act like one big hose — their rates simply ADD. The answer wants hours, so save yourself a conversion by building the combined rate in gallons-per-HOUR from the start.
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Hint 2 of 2
Once you have a single combined rate, time = total amount ÷ rate.
Show solution
Approach: combine rates, then divide total by rate
- One hose: 2.5 gal/min. Working together, rates add: 4 × 2.5 = 10 gal/min. Since the answer is in hours, scale up now: 10 gal/min × 60 = 600 gal/hour.
- Time = total ÷ rate = 24,000 ÷ 600 = 40 hours.
- Why this transfers: whenever several workers/pipes/machines run simultaneously, add their individual rates into one combined rate — then it's a single division. Converting units BEFORE dividing (here min→hr) avoids a clumsy 2,400-minute intermediate.
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