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

Answer:

1 inch : 5⅓ miles

6 inches

Step-by-step 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

Step-by-step explanation:

$\dfrac{\text{Model}}{\text{Actual}}:\dfrac{4\frac{1}{2}\ inches}{24\ miles}\div\dfrac{24}{24}=\dfrac{\frac{3}{16}}{1}\quad \longrightarrow \quad \large\boxed{\dfrac{3}{16}\ inches:1\ mile}$

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