An empty 1,200 gallon tank is filled with water at a rate of 6 gallons of water per minute. At the same time, another 1,200 gallon tank full of water is being drained at a rate of 9 gallons per minute. How many minutes will it take for the amount of water in both tanks to become the same?
Correct answer: B. 80
- A. 60
- B. 80
- C. 100
- D. 120
Explanation
To solve this problem, we need to equate the amount of water in both tanks after a certain time m minutes.Tank 1 starts empty and fills at 6 gallons per minute, so the amount of water in Tank 1 after m minutes is 6m.Tank 2 starts full at 1200 gallons and drains at 9 gallons per minute, so the amount of water in Tank 2 after m minutes is 1200 - 9m.Setting these equal gives: 6m = 1200 - 9mSolving for m gives:6m + 9m = 120015m = 1200m = 80Thus, after 80 minutes, both tanks will contain 480 gallons of water each. The other options do not satisfy this condition as calculated above.
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Quantitative reasoning applies arithmetic and basic algebra to numerical relationships, including percentages, ratios, averages, fractions, proportions, profit and loss, rates, time, work and measurement. Questions focus on translating words into equations, choosing an efficient method and checking whether the result is numerically reasonable.
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