HELP VERY URGENT

Question

The Transportation Department is planning a new section of interstate highway. For planning purposes, they are using a diagram with a scale 0.5 in : 10 mi. If the diagram shows the highway section to be 37 inches long, how long will the road actually be?

Answer 1

Hi Leen!I like to approach problems like this using a method I call "rules and tools". Consider the scale .5 in = 10 miles. This is an equality that is a "rule" for the drawing you are working with. Every "rule" or equality can be represented as two ratios that each equal 1. I call these "tools", because you can use them to solve the problem. Each tool is simply a fraction with the equality written in the numerator and denominator. For example, the "rule" .5 in = 10 miles can be written as .5 inches/10 miles or 10 miles/.5 inches. The two tools make it easy to go in either direction ie from scale to actual or from actual to scale.

In the problem you presented you be going from scale to actual, so you would multiply 37 inches by the fraction 10miles/.5 inches. In this way the inches "cancel out" and you have 37 x 10 = 370 divided by .5 which gives you 740. Notice that the miles have not canceled out so your final answer is 740 miles! Tip, it is always easier to visualize this if you write the fraction straight up and down instead of slanted with a slash, but I don't have that option within this part of the platform. In tutoring sessions there are more options and I use a document camera to help illustrate this very useful method. I hope this helped!