Since Curtis’s distance covered varies directly with the days he runs, we can set up a direct variation equation. This means that the distance $d$ he runs is directly proportional to the number of days $n$. In equation form, this can be written as:

$d = k \cdot n$

where $k$ is the constant of proportionality.

Step 1: Find the constant of proportionality ($k$)

From the problem, we know that in 4 days, Curtis ran 7 miles. Plugging these values into the equation:

$7 = k \cdot 4$

Solving for $k$:

$k = \frac{7}{4} = 1.75$

So, Curtis runs 1.75 miles per day.

Step 2: Calculate the distance for 11 days

Now that we know $k = 1.75$, we can find the distance he will cover in 11 days by substituting $n = 11$ into the equation:

$d = 1.75 \cdot 11$

$d = 19.25$

Therefore, Curtis will cover 19.25 miles in 11 days.

Would you like more details on how direct variation works, or have any questions?

Here are 5 related questions that explore similar concepts:

1. If Curtis ran for 15 days, how many miles would he cover?
2. How many days would it take Curtis to run a total of 35 miles at the same rate?
3. What would be the new distance in 11 days if Curtis increased his rate to 2 miles per day?
4. How is a direct variation different from an inverse variation in terms of distance and time?
5. How many miles would he run in half a day?

Tip: When dealing with direct variation problems, always start by finding the constant of proportionality (the rate), as it helps predict outcomes based on different input values.