Question

Emilio has to run 71
2
miles every week to train for the football team. If he runs 11
2
miles every day, how many days will
it take him to run 71
2
miles?



It will take Emilio
days to run 71
2
miles.

Answer 1

To find out how many days it will take Emilio to run \( \frac{71}{2} \) miles if he runs \( \frac{11}{2} \) miles every day, we can set up the following equation:

1. First, we need to determine how many miles he runs each day:
\[
\text{Daily miles} = \frac{11}{2} \text{ miles}
\]

2. Next, we need to determine the total number of miles he needs to run:
\[
\text{Total miles} = \frac{71}{2} \text{ miles}
\]

3. To find the number of days (\( d \)) it will take him to run \( \frac{71}{2} \) miles at the rate of \( \frac{11}{2} \) miles per day, we can use the formula:
\[
d = \frac{\text{Total miles}}{\text{Daily miles}} = \frac{\frac{71}{2}}{\frac{11}{2}}
\]

4. Dividing the two fractions:
\[
d = \frac{71}{2} \times \frac{2}{11} = \frac{71}{11}
\]

5. Now we can calculate \( \frac{71}{11} \):
\[
71 \div 11 = 6.454545... \text{ (approximately 6.45)}
\]

Since Emilio cannot run for a fraction of a day, we round this up to the nearest whole number, which gives us:
\[
d = 7 \text{ days}
\]

Thus, it will take Emilio **7 days** to run \( \frac{71}{2} \) miles.

**Final Answer: It will take Emilio 7 days to run \( \frac{71}{2} \) miles.**