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Difficulty: MediumUS Customary Linear Measurements

A civil engineer is evaluating four proposed segments for a new neighborhood walking trail. To properly allocate paving materials, the segments must be organized by length. Arrange the following trail segments in order from shortest to longest.

  1. 1Birch Path: 3,9003,900 inches
  2. 2Cedar Path: 108108 yards and 22 feet
  3. 3Elm Path: 116\frac{1}{16} of a mile
  4. 4Oak Path: 11012110 \frac{1}{2} yards

Answer

The correct order from shortest to longest is: Birch Path, Cedar Path, Elm Path, Oak Path.
By converting all distances to a common unit (feet), we find that Birch Path is 325 feet, Cedar Path is 326 feet, Elm Path is 330 feet, and Oak Path is 331.5 feet. Arranging these numbers from smallest to largest yields the correct sequence.

Step-by-Step Solution

1
Select a common unit of measurement to compare all segments.
Feet is the most practical common unit for these values.
Comparing different units (inches, yards, miles) directly leads to errors.
2
Convert Birch Path from inches to feet.
3,900÷12=3253,900 \div 12 = 325 feet.
There are 1212 inches in 11 foot.
3
Convert Cedar Path from yards and feet to total feet.
108×3=324108 \times 3 = 324 feet. Adding the remaining 22 feet gives 326326 feet.
There are 33 feet in 11 yard.
4
Convert Elm Path from miles to feet.
5,280×116=3305,280 \times \frac{1}{16} = 330 feet.
There are 5,2805,280 feet in 11 mile.
5
Convert Oak Path from yards to feet.
110.5×3=331.5110.5 \times 3 = 331.5 feet.
There are 33 feet in 11 yard, and 11012110 \frac{1}{2} can be written as 110.5110.5.
6
Order the converted values from smallest to largest.
325325 feet < 326326 feet < 330330 feet < 331.5331.5 feet.
The question asks for the order from shortest to longest.

Key Concept

Converting between US Customary linear measurements (inches, feet, yards, miles) to establish a common unit for comparison.
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Topics

US Customary Linear Measurements

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