How do you find the actual distances of these problems with a scale of 3/4" = 500 mi.
1 3/4"
14"
13"
3"
6"
You could set up a proportion. Cross multiply and solve for x.
0.75/500 = 1.75/x
0.75x = 875
x = 1,166.67 miles
1 3/4 = 7/4 inch
7/4 inch*(500 miles/.75 inch) = 1167 2/3 miles
14" (500mi/.75") = 9333 1/3 mi
etc
Now you know the math way and the science way :)
1166 2/3 I mean
To find the actual distances using a scale, you need to first determine the ratio between the scale and the actual distance. In this case, the given scale is 3/4" = 500 mi. This means that for every 3/4 inch on the map, the actual distance is 500 miles.
To find the actual distances, you can use the following steps:
1. Convert the fractional portion of the scale to decimal form: 3/4 = 0.75
2. Determine the actual distance represented by one inch on the map. Divide 500 miles by 0.75 (which is equivalent to 3/4) to get 666.6 miles per inch.
3. Multiply the measurement on the map by the actual distance represented by one inch.
Let's calculate the actual distances for the given measurements:
1 3/4": Multiply 1.75 inches by 666.6 miles/inch to get 1166.05 miles.
14": Multiply 14 inches by 666.6 miles/inch to get 9332.4 miles.
13": Multiply 13 inches by 666.6 miles/inch to get 8665.8 miles.
3": Multiply 3 inches by 666.6 miles/inch to get 1999.8 miles.
6": Multiply 6 inches by 666.6 miles/inch to get 3999.6 miles.
Therefore, the actual distances for the given measurements are:
- 1 3/4" = 1166.05 miles
- 14" = 9332.4 miles
- 13" = 8665.8 miles
- 3" = 1999.8 miles
- 6" = 3999.6 miles