To solve this, we can use the given scale to set up a proportion. The scale is $2.5$ centimeters on the map representing $15$ kilometers in real life. We want to find how many kilometers are represented by $17.5$ centimeters.

Let $x$ be the number of kilometers corresponding to $17.5$ centimeters. We set up the proportion as follows:

$\frac{2.5 \, \text{cm}}{15 \, \text{km}} = \frac{17.5 \, \text{cm}}{x \, \text{km}}$

Now, solve for $x$ by cross-multiplying:

$2.5 \cdot x = 15 \cdot 17.5$

$2.5 \cdot x = 262.5$

Now, divide both sides by $2.5$:

$x = \frac{262.5}{2.5} = 105$

So, $17.5$ centimeters on the map represents $105$ kilometers.

Do you want more details or have any questions? Here are 5 related questions for further practice:

1. If 3 centimeters represent 18 kilometers, how many kilometers does 9 centimeters represent?
2. If 5 centimeters on a map represent 40 kilometers, what is the actual distance for 12 centimeters?
3. What is the distance represented by 7.5 centimeters on a map with a scale of 2 cm = 10 km?
4. If a scale reads 1 cm = 5 km, how many centimeters would represent 50 km?
5. How do you convert a map scale of 1:50,000 to a verbal scale in kilometers?

Tip: Always remember to use proportions when dealing with map scales; they help in comparing different values accurately!