Question

A certain map shows two roads. Road A is 1 1/2 miles long but is 1 4/5 inches long on the map. What is the unit rate for inches per mile on this map? If road B is 15 miles long, how long is road B on the map?

Answer 1

To find the unit rate for inches per mile on a map, set up a proportion using the information for Road A. Convert the measurements to improper fractions if necessary. After calculating the unit rate, use it to determine the length of Road B on the map for a 15-mile actual distance.

Step-by-step explanation:

Understanding the Unit Rate on a Map

To determine the unit rate for inches per mile on a map, you can set up a proportion based on the lengths given for Road A. This map shows Road A as 1 1/2 miles long and 1 4/5 inches long on the map. The first step is to convert the mixed numbers to improper fractions. The unit rate can be calculated as follows:

1. Convert 1 1/2 miles to 3/2 miles.
2. Convert 1 4/5 inches to 9/5 inches.
3. Set up the proportion: (9/5) inches / (3/2) miles = x inches per mile.
4. Solve for x to find the unit rate.

Using the determined unit rate, you can then calculate the length of Road B on the map if it is 15 miles long in reality. The steps are:

1. Use the unit rate to set up another proportion.
2. Plug in 15 miles for the actual distance of Road B.
3. Solve for the map distance in inches.

This process allows you to accurately scale distances on the map to real-world distances and vice versa.