Question

On an Idaho map, 1 inch represents 20 miles. If the distance on the map

between two towns on the river measures 2 and 5-eighths inches, how many miles apart are the towns?

Answer options with 5 options
A.
42 and one-half miles

B.
45 miles

C.
47 and five-eighths miles

D.
52 and one-half miles

E.
40 miles

Answer 1

To find out how many miles apart the towns are, we first need to convert the measurement from inches to miles using the scale given on the map.

1 inch represents 20 miles. The distance measured between the towns is 2 and 5/8 inches.

First, we convert 2 and 5/8 inches to an improper fraction:
\[
2 \frac{5}{8} = \frac{2 \times 8 + 5}{8} = \frac{16 + 5}{8} = \frac{21}{8}
\]

Next, we multiply this distance by the scale of miles per inch:
\[
\text{Distance in miles} = \left(\frac{21}{8} \text{ inches}\right) \times 20 \text{ miles/inch}
\]

Calculating this:
\[
\text{Distance in miles} = \frac{21 \times 20}{8} = \frac{420}{8} = 52.5 \text{ miles}
\]

52.5 miles can also be expressed as \( 52 \frac{1}{2} \) miles.

Hence, the towns are **52 and one-half miles** apart.

The correct answer is **D. 52 and one-half miles**.