Question

Last week, Ernesto ran 2 1/5 miles. This week, he plans to run 4 3/4 times as far as last week. How many miles does Ernesto plan to run this week?

Write your answer as a fraction or as a whole or mixed number.

Answer 1

To determine how far Ernesto plans to run this week, we first need to calculate \( 4 \frac{3}{4} \) times the distance he ran last week, which is \( 2 \frac{1}{5} \) miles.

1. Convert the mixed numbers to improper fractions:

For \( 2 \frac{1}{5} \):
\[
2 \frac{1}{5} = 2 \times 5 + 1 = 10 + 1 = 11 \quad \text{(improper fraction: } \frac{11}{5})
\]

For \( 4 \frac{3}{4} \):
\[
4 \frac{3}{4} = 4 \times 4 + 3 = 16 + 3 = 19 \quad \text{(improper fraction: } \frac{19}{4})
\]

2. Now calculate \( \frac{19}{4} \times \frac{11}{5} \):
\[
\frac{19}{4} \times \frac{11}{5} = \frac{19 \times 11}{4 \times 5} = \frac{209}{20}
\]

3. We can convert \( \frac{209}{20} \) to a mixed number:

- Divide \( 209 \) by \( 20 \):
\[
209 \div 20 = 10 \quad \text{(with a remainder of } 9\text{)}
\]
- So, \( 209 = 20 \times 10 + 9 \), which yields the mixed number:
\[
10 \frac{9}{20}
\]

Thus, the distance Ernesto plans to run this week is \( \boxed{10 \frac{9}{20}} \).