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A city planner is budgeting for emergency highway repairs. The portion of the highway that needs to be repaired is 3.1 miles 14.1 feet long. How long is this in yards, feet, and inches?

Round the inches to the nearest tenth.

Conversion ratios:
- [tex]$1 \text{ mi} =1,760 \text{ yd}$[/tex]
- [tex]$3 \text{ ft} =1 \text{ yd}$[/tex]
- [tex]12 \text{ in.} =1 \text{ ft}$[/tex]

A. [tex]5,456 \text{ yd} \, 12 \text{ ft} \, 1.2 \text{ in.}[/tex]
B. [tex]5,460 \text{ yd} \, 2 \text{ ft} \, 1.2 \text{ in.}[/tex]
C. [tex]5,460 \text{ yd} \, 1 \text{ ft} \, 11.7 \text{ in.}[/tex]

Sagot :

GinnyAnswer
To determine the length of the highway portion in yards, feet, and inches, we need to follow a few conversion steps:

1. Convert miles to yards:
- We know that 1 mile is equivalent to 1,760 yards.
- Given that the highway segment is 3.1 miles long, we calculate the yards from miles:
[tex]\[ 3.1 \text{ miles} \times 1760 \text{ yards/mile} = 5456 \text{ yards} \][/tex]

2. Convert the remaining feet to yards and feet:
- The additional portion of the highway is 14.1 feet.
- Every 3 feet equals 1 yard.
- First, calculate how many full yards are in 14.1 feet:
[tex]\[ 14.1 \text{ feet} \div 3 \text{ feet/yard} = 4 \text{ yards and} 2.1 \text{ feet remaining} Therefore, the feet portion is split into 4 yards and 2.1 feet. \][/tex]

3. Total yards:
- Add the yards from miles and the yards from feet:
[tex]\[ 5456 \text{ yards} + 4 \text{ yards} = 5460 \text{ yards} \][/tex]

4. Convert remaining feet to inches:
- There are 2.1 feet remaining.
- Since 1 foot equals 12 inches, convert the remaining feet to inches:
[tex]\[ 2.1 \text{ feet} \times 12 \text{ inches/foot} = 25.2 \text{ inches} \][/tex]

Now, we can compile the final lengths:
- Total length in yards: 5460 yards
- Remaining feet: 2.1 feet (approximately 2 feet due to the rounding in conversion calculations)
- Remaining inches: 25.2 inches

Therefore, the correct length of the highway portion in the requested format is:

B) 5,460 yd 2 ft 25.2 in
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