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?

Question

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 $2\frac{1}{5}$: $$2\frac{1}{5}=2\times 5+1=10+1=11\text{(improper fraction: }\frac{11}{5})$$

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

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 $20$: $$209÷20=10\text{(with a remainder of }9\text{)}$$
   • 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 $\boxed{{\displaystyle 10\frac{9}{20}}}$.