Alright, let's go through the problem step-by-step.
Elena ran [tex]\( 2 \frac{1}{2} \)[/tex] miles.
### Part a: Converting miles to feet
To find out how many feet this distance represents, we'll use the conversion factor that 1 mile equals 5,280 feet.
1. First, convert the mixed number [tex]\( 2 \frac{1}{2} \)[/tex] to an improper fraction or a decimal.
[tex]\[ 2 \frac{1}{2} = 2 + \frac{1}{2} = 2.5 \text{ miles} \][/tex]
2. Next, multiply the number of miles by the number of feet in a mile.
[tex]\[ 2.5 \text{ miles} \times 5,280 \text{ feet/mile} = 13,200 \text{ feet} \][/tex]
So, [tex]\( 2 \frac{1}{2} \)[/tex] miles is equal to 13,200 feet.
### Part b: Converting feet to inches
Now, we'll convert the number of feet to inches, using the conversion factor that 1 foot equals 12 inches.
1. Multiply the number of feet by the number of inches in a foot.
[tex]\[ 13,200 \text{ feet} \times 12 \text{ inches/foot} = 158,400 \text{ inches} \][/tex]
So, [tex]\( 2 \frac{1}{2} \)[/tex] miles is equal to 158,400 inches.
Therefore, Elena ran 158,400 inches.
