Alright, let's solve this step-by-step.
### Step 1: Convert 2.4 feet to yards
First, we need to convert 2.4 feet into yards. We know that there are 3 feet in 1 yard. So, we will divide the feet by the conversion ratio to get yards:
[tex]\[
\text{Yards from feet} = \frac{2.4 \text{ feet}}{3 \text{ feet/yard}} = 0.8 \text{ yards}
\][/tex]
### Step 2: Convert total distance in yards to miles
Next, we need to add the converted yards from the feet to the total yards given. Then, we'll convert the entire distance from yards to miles. We know we have 4,133 yards originally, so we add the 0.8 yards:
[tex]\[
\text{Total distance in yards} = 4133 + 0.8 = 4133.8 \text{ yards}
\][/tex]
Now, we need to convert the total distance into miles. We know there are 1,760 yards in a mile:
[tex]\[
\text{Total miles} = \frac{4133.8 \text{ yards}}{1760 \text{ yards/mile}} \approx 2.35 \text{ miles}
\][/tex]
### Step 3: Convert the decimal of miles to yards
Now, we take the decimal part of the miles (0.35 miles) and convert it back to yards to find the remaining distance in yards:
[tex]\[
\text{Remaining distance in yards} = 0.35 \text{ miles} \times 1760 \text{ yards/mile} \approx 616 \text{ yards}
\][/tex]
### Step 4: Convert the decimal of yards to feet
Next, we take the decimal part of the 616 yards (0.8 yards) and convert it to feet. We know 1 yard = 3 feet:
[tex]\[
\text{Remaining distance in feet} = 0.8 \text{ yards} \times 3 \text{ feet/yard} = 2.4 \text{ feet}
\][/tex]
Finally, we need to convert the decimal part of the feet (0.4 feet) to inches. We know 1 foot = 12 inches:
[tex]\[
\text{Remaining distance in inches} = 0.4 \text{ feet} \times 12 \text{ inches/foot} = 4.8 \text{ inches}
\][/tex]
### Summary
So, our calculations tell us that the total distance of the subway in miles, feet, and inches is:
- Miles: [tex]\(2\)[/tex]
- Feet: [tex]\(2\)[/tex]
- Inches: [tex]\(4.8\)[/tex]
Therefore, the length of the subway is [tex]\(2\)[/tex] miles, [tex]\(2\)[/tex] feet, and [tex]\(4.8\)[/tex] inches.
