Question

Giovanni went to Los Angeles, California for the summer to visit his cousins. He used a map of bus routes to get from the airport to his cousins house. The distance from the airport to his cousins house is 56 km. On his map, the distance is 4 cm. What is the scale factor?

Answer 1

56 / 4 = 14

1 cm = 14 km

Answer 2

Answer: $scale\ factor=\frac{1}{1,400,000}$

Step-by-step explanation:

You know that, on Giovanni's map, the distance from the airport to his cousin's house is 4 centimeters and the actual distance from the the airport to his cousin's house is 56 kilometers.

Then, in order to find the scale factor, the first step is to make the conversion from kilometers to centimeters.

It is important to remember that:

$1\ kilometer=100,000\ cm$

Therefore, 56 kilometers to centimeters is:

$(56\ km)(\frac{100,000\ cm}{1\ km})=5,600,000\ cm$

Then, the scale factor is:

$scale\ factor=\frac{4}{5,600,000\ cm}\\\\scale\ factor=\frac{1}{1,400,000}$