The distance walked varies directly to the speed you are walking. If you can walk 3 miles in 33 minutes, how many miles can walk in 209 minutes?

The relationship between the distance walked and the time spent walking is directly proportional to the speed. This means the ratio of distance to time remains constant.

We are given:
- 3 miles in 33 minutes
- We need to find how many miles can be walked in 209 minutes.

Let's denote:
- \( d_1 = 3 \) miles (distance walked in 33 minutes),
- \( t_1 = 33 \) minutes,
- \( t_2 = 209 \) minutes,
- \( d_2 \) as the unknown distance for 209 minutes.

The direct variation formula is:

\[
\frac{d_1}{t_1} = \frac{d_2}{t_2}
\]

Substituting the known values:

\[
\frac{3}{33} = \frac{d_2}{209}
\]

Solve for \( d_2 \):

\[
d_2 = \frac{3}{33} \times 209 = \frac{209}{11} \approx 19
\]

So, you can walk approximately **19 miles** in 209 minutes.

Would you like further clarification or a detailed explanation? 

Here are some related questions:
1. How do you calculate direct variation in general?
2. How does the ratio between time and speed affect the total distance?
3. Can we convert minutes into hours and solve the same problem?
4. How would the answer change if you had breaks during the 209 minutes?
5. What other types of variations exist besides direct proportionality?

**Tip**: To work with proportions efficiently, keep the ratios in fractions to avoid rounding errors until the final step.

The distance walked varies directly to the speed you are walking. If you can walk 3 miles in 33 minutes, how many miles can you walk in 209 minutes?

Solve how many miles you can walk in 209 minutes if you walk 3 miles in 33 minutes. This problem involves direct proportion and the ratio between distance and time. Suitable for students in Grades 6-8.

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