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Difficulty: MediumUS Customary Linear Measurements

A stage crew is connecting two sections of metal piping end-to-end to build a vertical pole for a lighting rig. The bottom section is 2122 \frac{1}{2} yards long. The top section is 44 feet 66 inches long. What is the total height of the assembled pole in yards?

  1. A
    3123 \frac{1}{2}
  2. 44Answer
  3. C
    77
  4. D
    1616

Answer

The total height of the assembled pole is 44 yards.
To find the total height, both measurements must be converted to the same unit. The top section is 44 feet 66 inches, which is exactly 4.54.5 feet. Since there are 33 feet in a yard, dividing 4.54.5 by 33 yields 1.51.5 yards (or 1121 \frac{1}{2} yards). Adding this to the bottom section's length of 2122 \frac{1}{2} yards gives exactly 44 yards.

Step-by-Step Solution

1
Convert the length of the top section from feet and inches to a single unit (feet).
44 feet 66 inches equals 4.54.5 feet (since 66 inches is half of a foot).
It is necessary to express the length in a uniform unit before converting it to yards.
2
Convert the top section's length from feet to yards.
4.54.5 feet divided by 33 feet per yard equals 1.51.5 yards (or 1121 \frac{1}{2} yards).
The final requested answer is in yards, so both sections must be expressed in this unit.
3
Add the lengths of both sections in yards.
212 yards+112 yards=4 yards2 \frac{1}{2} \text{ yards} + 1 \frac{1}{2} \text{ yards} = 4 \text{ yards}.
Connecting the pipes end-to-end means their total combined height is the sum of their individual lengths.

Key Concept

Converting mixed linear measurements (feet and inches) to yards and adding fractional quantities.

Alternative Method

Convert all measurements to inches first. The bottom section is 2122 \frac{1}{2} yards, which is 2.5×36=902.5 \times 36 = 90 inches. The top section is 44 feet 66 inches, which is 48+6=5448 + 6 = 54 inches. Add them together to get 144144 inches. Finally, divide by 3636 inches per yard to get exactly 44 yards.
Estimated Time:1m 0s
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Topics

US Customary Linear Measurements

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