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Difficulty: MediumUS Customary Linear Measurements

A communications technician is preparing four different runs of fiber optic cable for an office building installation. To organize the work, the technician must sort the cable runs from shortest to longest.

Run 1: 115115 yards and 22 feet
Run 2: 4,1884,188 inches
Run 3: 115\frac{1}{15} of a mile
Run 4: 350350 feet and 66 inches

Arrange the cable runs in order from shortest to longest.

  1. 1Run 1: 115115 yards and 22 feet
  2. 2Run 2: 4,1884,188 inches
  3. 3Run 4: 350350 feet and 66 inches
  4. 4Run 3: 115\frac{1}{15} of a mile

Answer

The correct order from shortest to longest is: Run 1, Run 2, Run 4, and Run 3.
By converting all lengths to a common unit (feet), we can directly compare them. Run 1 is 347347 feet, Run 2 is 349349 feet, Run 4 is 350.5350.5 feet, and Run 3 is 352352 feet. Ordering these from smallest to largest yields the correct sequence: Run 1, Run 2, Run 4, Run 3.

Step-by-Step Solution

1
Convert the length of Run 1 into feet.
347347 feet
Since 11 yard equals 33 feet, multiply 115115 yards by 33 to get 345345 feet. Add the additional 22 feet for a total of 347347 feet.
2
Convert the length of Run 2 into feet.
349349 feet
Since 11 foot equals 1212 inches, divide 4,1884,188 inches by 1212 to get 349349 feet.
3
Convert the length of Run 3 into feet.
352352 feet
Since 11 mile equals 5,2805,280 feet, divide 5,2805,280 by 1515 (or multiply by 115\frac{1}{15}) to get 352352 feet.
4
Convert the length of Run 4 into feet.
350.5350.5 feet
Since 66 inches is exactly 12\frac{1}{2} of a foot, the measurement is 350.5350.5 feet.
5
Compare the standardized lengths and order them from shortest to longest.
Run 1 (347347 ft) < Run 2 (349349 ft) < Run 4 (350.5350.5 ft) < Run 3 (352352 ft)
Comparing all measurements in a common unit (feet) reveals the final correct sequence.

Key Concept

Converting mixed US Customary linear units (inches, feet, yards, miles) to a single common unit to compare their lengths.
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Topics

US Customary Linear Measurements

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