ⓐ Read the problem. Draw the figures and label with the given information.

The figures are shown in the question.

Identify what we are looking for: the actual distance from San Antonio to Columbus.

Name the variables.

Let $x$ = distance from San Antonio to Columbus.

Translate into an equation. Since the triangles are similar, the corresponding sides are proportional. We’ll make the numerators "miles" and the denominators "inches."

$\frac{\text{x mi}}{\mathrm{6.6\; in}}=\frac{\mathrm{802\; mi}}{\mathrm{4.8\; in}}$

Solve the equation.

$\frac{x}{6.6}=\frac{802}{4.8}$

$x=802·\frac{6.6}{4.8}=\mathrm{1102.8\; mi}$

Check.

Check $x=\mathrm{1102.8\; mi}$ in the original proportion.

$\frac{\text{x mi}}{\mathrm{6.6\; in}}=\frac{\mathrm{802\; mi²}}{\mathrm{4.8\; in}}$

$\frac{\mathrm{1102.8\; mi}}{\mathrm{6.6\; in}}$ $\stackrel{?}{=}$ $\frac{\mathrm{802\; mi}}{\mathrm{4.8\; in}}$

$\frac{\mathrm{802\; mi}}{\mathrm{4.8\; in}}$ $\stackrel{?}{=}$ $\frac{\mathrm{802\; mi}}{\mathrm{4.8\; in}}$ ✓

Answer the question.

The distance from San Antonio to Columbus is $1102.8$ miles.

ⓑ Read the problem. Draw the figures and label with the given information.

The figures are shown in the question.

Identify what we are looking for: the actual distance from Omaha to Columbus.

Name the variables.

Let $y$ = distance from Omaha to Columbus.

Translate into an equation. Since the triangles are similar, the corresponding sides are proportional. We’ll make the numerators "miles" and the denominators "inches."

$\frac{\text{y mi}}{\mathrm{4\; in}}=\frac{\mathrm{802\; mi}}{\mathrm{4.8\; in}}$

Solve the equation.

$\frac{y}{4}=\frac{802}{4.8}$

$y=802·\frac{4}{4.8}=\mathrm{668.3\; mi}$

Check.

Check $y=\mathrm{668.3\; mi}$ in the original proportion.

$\frac{\text{y mi}}{\mathrm{4\; in}}=\frac{\mathrm{802\; mi²}}{\mathrm{4.8\; in}}$

$\frac{\mathrm{668.3\; mi}}{\mathrm{4\; in}}$ $\stackrel{?}{=}$ $\frac{\mathrm{802\; mi}}{\mathrm{4.8\; in}}$

$\frac{\mathrm{802\; mi}}{\mathrm{4.8\; in}}$ $\stackrel{?}{=}$ $\frac{\mathrm{802\; mi}}{\mathrm{4.8\; in}}$ ✓

Answer the question.

The distance from Omaha to Columbus is $668.3$ miles.