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Difficulty: HardRectangular Volume and Container Capacity

A rectangular reservoir for a water purification system measures 2020 feet long, 1515 feet wide, and 1010 feet deep. Safety protocols dictate that the reservoir must never exceed 90%90\% of its total volume capacity. The reservoir currently contains 900900 cubic feet of water. If a high-capacity pump adds water to the reservoir at a rate of 6060 cubic feet per minute, how many minutes will it take for the water to reach the maximum allowed capacity?

Answer: 30 minutes

Answer

30
First, the total volume of the rectangular reservoir is found by multiplying its length, width, and depth (20×15×10=300020 \times 15 \times 10 = 3000 cubic feet). Next, the maximum allowed capacity is determined by finding 90%90\% of the total volume (0.90×3000=27000.90 \times 3000 = 2700 cubic feet). Since the reservoir already contains 900900 cubic feet of water, the exact amount needed to reach the maximum safe capacity is the difference (2700−900=18002700 - 900 = 1800 cubic feet). Finally, the time required to add this volume at a rate of 6060 cubic feet per minute is calculated by dividing the needed volume by the pump's rate (1800÷60=301800 \div 60 = 30 minutes).

Step-by-Step Solution

1
Calculate the total volume of the reservoir.
20×15×10=300020 \times 15 \times 10 = 3000 cubic feet
The total volume is required to determine what the absolute maximum capacity is before applying the percentage limit.
2
Calculate the maximum allowed capacity.
3000×0.90=27003000 \times 0.90 = 2700 cubic feet
Safety protocols dictate the reservoir cannot exceed 90%90\% of its total physical volume.
3
Determine the required volume of water to add.
2700−900=18002700 - 900 = 1800 cubic feet
The reservoir already contains 900900 cubic feet of water, so we only need to pump the difference to reach the safe limit.
4
Calculate the time required to fill the reservoir to the required level.
1800÷60=301800 \div 60 = 30 minutes
Time is calculated by dividing the total volume to be added by the filling rate of the pump.

Key Concept

Calculating rectangular volume, applying percentage constraints to capacity, and solving for time using a given rate.
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Topics

Rectangular Volume and Container Capacity

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