Instructions: read the problem. Then answer the questions. 1. Imagine you are looking at a map of the United States, but it does not have a scale that indicates the number of miles per inch. You use a ruler to measure the distance between New York City and Washington D.C. in the map. the distance is 2 1/2 inches. You consult a website and find out that the real distance between New York City and Washington DC is. it is 200 miles. A. What is the scale of the map in miles per inch (unit rate)?_ B. Write the equation of the proportional relationship whose constant of proportionality is the scale of the map. It states that the Y represents the distance in miles and the X represents this distance on the map in inches. C. Using a ruler, you determine that the distance between New York City and Atlanta on the map is 8.75 inches. What is the actual distance between New York City and Atlanta in miles?______

Question

contestada

Respuesta :

NakitaN67637 NakitaN67637 · Answer 1 · 2022-10-28T03:17:09+02:00

Given:

Distance between New york and Washington DC in ruler is, d(r) = 2 1/2 inches=2.5 inches.

Actual distance between New york and Washington DC is, d(a) = 200 miles.

The objective is,

a) To find the scale ratio of map

b) To write the equation of relationship

c) To find the actual distance if distance between New york and Atlanta in map is 8.75 inches.

a)

The scale ratio can be calculated as,

[tex]\begin{gathered} r=\frac{d(a)}{d(r)} \\ r=\frac{200}{2.5} \\ r=80\text{ miles per inch.} \end{gathered}[/tex]

Hence, the scale ratio of map is 80 miles per inch.

b)

Consider the actual distance as Y (miles) and the distance in map as X (inches).

The equation can be represented as,

[tex]\begin{gathered} Y\propto X \\ Y=rX \end{gathered}[/tex]

Here, r represents the proportionality contant which is the scale ratio of the map.

Hence, the required equation is Y = rX.

c)

The actual distance between New York City and Atlanta can be calculated using the equation obtained in part (b).

It is known that r = 80 miles per inch and the value of X is given as 8.75 inches.

Substitute the obtained values in the equation.

[tex]\begin{gathered} Y=80\cdot8.75 \\ Y=700\text{ miles} \end{gathered}[/tex]

Hence, the actual distance between New York City and Atlanta is 700 miles.