On a map, 1 inch equals 5.4 miles. Two houses are 1.5 inches apart on the map. What is the actual distance between the houses? Use pencil and paper. Show how you can represent the scale with two different ratios. What ratio is more helpful for solving the problem? Explain.
To find the actual distance between the two houses, we first need to determine the scale factor by which we can convert the map distance to actual distance.
Using the given scale where 1 inch on the map equals 5.4 miles in real life, we can set up two different ratios:
1. Ratio 1:
1 inch on map = 5.4 miles in reality
1.5 inches on map = x miles in reality
We can solve for x by setting up a proportion:
1/5.4 = 1.5/x
x = 1.5 * 5.4 = 8.1 miles
2. Ratio 2:
1 inch on map = 5.4 miles in reality
5.4 miles in reality = 1 inch on map
Therefore, 1.5 inches on the map = 5.4 miles * 1.5 = 8.1 miles
Comparing the two ratios, we see that the second ratio is more helpful for solving the problem as it directly relates the distance in inches on the map to the distance in miles in reality. This ratio simplifies the process and makes it easier to understand the relationship between the two distances.