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Difficulty: MediumRectangular Volume and Container Capacity

An engineer battalion is excavating a rectangular subterranean bunker. The excavated space must be 120120 feet long, 3030 feet wide, and 1515 feet deep. If the earth-moving equipment removes soil at a rate of 200200 cubic yards per hour, how many hours will it take to complete the excavation?

  1. A
    270
  2. B
    90
  3. C
    18
  4. 10Answer

Answer

It will take 10 hours to complete the excavation.
The correct answer is 1010. To find the time required, we must determine the total volume of the bunker in cubic yards, since the removal rate is given in cubic yards per hour. First, convert the dimensions from feet to yards by dividing by 33: the length is 4040 yards, the width is 1010 yards, and the depth is 55 yards. The volume is 40×10×5=2,00040 \times 10 \times 5 = 2,000 cubic yards. Dividing the total volume of 2,0002,000 cubic yards by the rate of 200200 cubic yards per hour yields 1010 hours.

Step-by-Step Solution

1
Convert the bunker dimensions from feet to yards.
Length = 4040 yards, Width = 1010 yards, Depth = 55 yards.
The removal rate is given in cubic yards, so calculating the volume directly in cubic yards simplifies the problem.
2
Calculate the total volume of the bunker.
40 yd×10 yd×5 yd=2,00040 \text{ yd} \times 10 \text{ yd} \times 5 \text{ yd} = 2,000 cubic yards.
The total volume represents the amount of soil that needs to be removed.
3
Calculate the time required by dividing the volume by the removal rate.
2,000 yd3÷200 yd3/hr=102,000 \text{ yd}^3 \div 200 \text{ yd}^3/\text{hr} = 10 hours.
Time is equal to the total volume divided by the rate of work.

Key Concept

Converting linear dimensions to calculate volume in a specific unit, and using rates to find time.

Alternative Method

Instead of converting the linear dimensions first, you can calculate the volume in cubic feet (120×30×15=54,000 ft3120 \times 30 \times 15 = 54,000 \text{ ft}^3), convert the removal rate to cubic feet per hour (200 yd3/hr×27 ft3/yd3=5,400 ft3/hr200 \text{ yd}^3/\text{hr} \times 27 \text{ ft}^3/\text{yd}^3 = 5,400 \text{ ft}^3/\text{hr}), and then divide: 54,000÷5,400=1054,000 \div 5,400 = 10 hours.
Estimated Time:1m 30s
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Topics

Rectangular Volume and Container Capacity

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