Question

a u.s. geological survey map has a scale of 1:21800. if two buildings are 3.57 miles apart, how many inches apart are they on the map? they are \boxed{} inches apart on the map.

Explanation:

Step1: Convert miles to inches

First, convert the real-world distance from miles to inches. We know 1 mile = 5280 feet, 1 foot = 12 inches, so:
$3.57 \text{ miles} = 3.57 \times 5280 \times 12 \text{ inches} = 3.57 \times 63360 = 226195.2 \text{ inches}$

Step2: Apply map scale

The scale 1:21800 means 1 map inch = 21800 real inches. Calculate map distance:
$\text{Map distance} = \frac{\text{Real distance}}{21800} = \frac{226195.2}{21800}$

Step3: Compute final value

Perform the division:
$\frac{226195.2}{21800} \approx 10.376$

Answer:

10.38 (rounded to two decimal places, or 10.39/10.4 depending on rounding precision; the precise calculated value is ~10.376)