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Question

Difficulty: HardDirect Proportions

A combat engineering team lays 180180 feet of portable runway surface every 2020 minutes. If they continue working at this exact same constant rate, how many yards of runway surface can they lay during a standard 55-hour shift?

  1. A
    4
  2. B
    15
  3. 900Answer
  4. D
    2,700

Answer

900
First, find the unit rate of runway laid per minute by dividing the given distance by the given time (180 feet÷20 minutes=9 feet per minute180 \text{ feet} \div 20 \text{ minutes} = 9 \text{ feet per minute}). Next, convert the total shift time from hours to minutes (5 hours×60 minutes/hour=300 minutes5 \text{ hours} \times 60 \text{ minutes/hour} = 300 \text{ minutes}). Multiply the unit rate by the total minutes to find the total distance in feet (9 feet/minute×300 minutes=2,700 feet9 \text{ feet/minute} \times 300 \text{ minutes} = 2,700 \text{ feet}). Finally, convert feet to yards by dividing by 33 (2,700 feet÷3 feet/yard=900 yards2,700 \text{ feet} \div 3 \text{ feet/yard} = 900 \text{ yards}).

Step-by-Step Solution

1
Determine the unit rate of construction in feet per minute.
180 feet÷20 minutes=9 feet per minute180 \text{ feet} \div 20 \text{ minutes} = 9 \text{ feet per minute}
Finding the unit rate allows for easy calculation of distance over any given amount of time.
2
Convert the total shift time from hours to minutes.
5 hours×60 minutes/hour=300 minutes5 \text{ hours} \times 60 \text{ minutes/hour} = 300 \text{ minutes}
The unit rate is in feet per minute, so the total time must also be in minutes to maintain consistent units.
3
Calculate the total distance constructed in feet.
9 feet/minute×300 minutes=2,700 feet9 \text{ feet/minute} \times 300 \text{ minutes} = 2,700 \text{ feet}
Multiplying the rate by the total time gives the total amount of surface laid.
4
Convert the total distance from feet to yards.
2,700 feet÷3 feet/yard=900 yards2,700 \text{ feet} \div 3 \text{ feet/yard} = 900 \text{ yards}
The question specifically asks for the final answer in yards, requiring division by 33.

Key Concept

Direct proportions with multiple unit conversions

Alternative Method

Instead of breaking the problem down into steps, you can set up a single dimensional analysis equation: 180 ft20 min×60 min1 hr×5 hr1×1 yd3 ft=900 yd\frac{180 \text{ ft}}{20 \text{ min}} \times \frac{60 \text{ min}}{1 \text{ hr}} \times \frac{5 \text{ hr}}{1} \times \frac{1 \text{ yd}}{3 \text{ ft}} = 900 \text{ yd}.
Estimated Time:2m 0s
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Topics

Direct Proportions

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