Question

The distance between two cities on a map is 4 1/2 inches. The actual distance between the two cities is 24 miles.

What is the scale used on the map?
If the scale on a different map of the same area is 1/4 inch = 1 mile, how many inches separate the same two cities?

Answer 1

1 inch : 5⅓ miles

6 inches

Explanation:

Map : Actual

4½ : 24

1 : 24/4.5

24 ÷ 9/2 = 24 × 2/9 =

1 inch on map represents an actual distance of 16/3 miles in actual

16/3 = 5⅓ miles

Map : Actual

¼ inch : 1 mile

X inch : 24

¼×24 = 6 inches

Answer 2

Answer: 3/16 inches : 1 mile

6 inches

Explanation:

`\frac{\text{Model}}{\text{Actual}}:(4(1)/(2)\ inches)/(24\ miles)/(24)/(24)=((3)/(16))/(1)\quad \longrightarrow \quad \large\boxed{(3)/(16)\ inches:1\ mile}\\`

`\frac{\text{Model}}{\text{Actual}}:((1)/(4)\ inches)/(1\ mile)=(x)/(24\ miles)\\\\\\\text{Cross Multiply}:\quad (1)/(4)\bigg(24\bigg)=x\\\\.\qquad \qquad \qquad \qquad \quad \quad \large\boxed{6=x}`