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
