Question

On a hiking trail​ map, the distance from mountain peak A to mountain peak B is 12.3 inches. The actual distance is about​ 1,000 miles. What is the distance on the same map from river A to river B if the actual distance is about 100​ miles?

Answer 1

Using a derived map scale from the known distance between two peaks, the map distance between river A and river B is calculated to be 1.23 inches based on the scale proportion of 12.3 inches representing 1,000 miles.

Step-by-step explanation:

The question relates to the concept of map scale which is often addressed in mathematics, specifically in topics involving ratios and proportions. To find the distance on the map from river A to river B, we need to use the map's scale that we derive from the given information.

Firstly, we determine the scale based on the distance between mountain peak A and B. The map shows 12.3 inches for 1,000 miles. Then, we use a proportion to find the map distance for 100 miles, which is the actual distance between river A and B.

The scale can be expressed as:

1 inch / (1,000 miles / 12.3 inches) = X inches / 100 miles

Now we solve for X:

X = (100 miles * 12.3 inches) / 1,000 miles = 1.23 inches

So, the distance on the map between river A to river B is 1.23 inches.

Answer 2

The distance of the rivers on the map is of 1.23 inches.

Step-by-step explanation:

We use proportions to solve this question, by a rule of three.

We have that:

If the actual distance is of 1000 miles, the distance on the map is of 12.3 inches. If the actual distance is 100 miles, what will be the distance on the map?

1000 miles - 12.3 inches

100 miles - x

Applying cross multiplication

`1000x = 12.3*100`

`1000x = 1230`

`x = (1230)/(1000)`

`x = 1.23`

The distance of the rivers on the map is of 1.23 inches.