Question

The starting and finish lines for a race in Fulton are 21 centimeters apart on a map of the course. If the scale of the map is 7 centimeters : 4 kilometers, then what is the actual distance between the starting line and the finish line?

Answer 1

84 km

Step-by-step explanation

A scale factor in math is the ratio between corresponding measurements of an object and a representation of that object

`sf\text{ =}\frac{\text{object}}{\text{representa}}`

in this case, the object is the real terrain and the representation is the map.

Step 1

find the scale factor

a) convert 4 kilometers into centimeters ( use equivalent fractions)

`\begin{gathered} 4\text{ km(}\frac{1000\text{ m}}{1\text{ Km}}\text{)(}\frac{100\text{ cm}}{1m}) \\ 400000\text{ cm} \end{gathered}`

so

the scale factor is

`\begin{gathered} sf\text{ =}\frac{\text{4}00000\text{ cm}}{\text{7 cm}} \\ sf\text{ =}\frac{\text{4}00000\text{ }}{\text{7 }} \\ \end{gathered}`

Step 2

now, to find a measure in the reality ( in cm) in the map we need to find the measure ( in the map) by the scale factor ,so

21 cm

`21\text{ cm}\cdot(\frac{400000cm_(real)}{1\text{ m}})=8400000\text{ cm}`

now, to convert from cm to kilometers, divide by 100000

so

`\begin{gathered} 8400000\text{ cm} \\ 8400000\text{ cm}\cdot(\frac{1\text{ km}}{100000\text{ cm}})=84 \end{gathered}`

therefore, the answer is 84 km

I hope this helps you