Question

if the scale in the drawing is 1/4inch=3miles, what is the distance, in miles between Hawthorne an Doylestown?(help)

Answer 1

We will investigate how to use ratios to determine the actual distance between cities as per defined scale.

We are given a scale conversion ( ratio ) at which distances are scaled down:

`\begin{gathered} \text{Scale : Actual} \\ (3)/(4)\text{ in : }3\text{ miles} \end{gathered}`

We will use the given scale ratio to determine the actual distance between two citites. The scale distance between Hawthorne and Doyelstown can be read.

`\text{Scale distance = 1.75 in}`

Now utilize the scale conversion ratio to determine the actual distance:

`\begin{gathered} \text{Scale : Actual } \\ (3)/(4)in\text{ : 3 miles} \\ \\ 1.75\text{ in: x} \\ ======= \\ \\ (3)/(4)\cdot x\text{ = 3}\cdot1.75 \\ \\ x\text{ = }(3\cdot1.75\cdot4)/(3) \\ \\ x\text{ = 7 miles} \end{gathered}`

Therefore, the distance between Hawthorne and Doylestown is:

`7\text{ miles}`