Question

A map shows the distance between Dallas and Houston as 2 inches. The actual distance is 240 miles. If there are 63,360 inches in a mile, find the ratio of the distance on the map to the actual distance between Dallas and Houston.

Answer 1

To determine the ratio of the distance on the map to the actual distance between Dallas and Houston, follow these steps:

1. **Calculate the actual distance in inches:**
The actual distance between Dallas and Houston is 240 miles. Since there are 63,360 inches in a mile, the total distance in inches can be calculated as:
\[
240 \text{ miles} \times 63,360 \text{ inches/mile} = 15,206,400 \text{ inches}
\]

2. **Given distance on the map:**
The map shows the distance as 2 inches.

3. **Form the ratio:**
The ratio of the distance on the map to the actual distance is:
\[
\text{Ratio on map to actual distance} = \frac{2 \text{ inches}}{15,206,400 \text{ inches}}
\]

4. **Simplify the ratio:**
Divide both the numerator and the denominator by 2:
\[
\frac{2 \text{ inches}}{15,206,400 \text{ inches}} = \frac{1 \text{ inch}}{7,603,200 \text{ inches}}
\]

Thus, the ratio of the distance shown on the map to the actual distance between Dallas and Houston is:
\[
\boxed{\frac{1}{7,603,200}}
\]