To determine the actual distance between City C and City D based on the distances given on the map, we first need to calculate the scale of the map.
The scale of the map can be calculated as follows:
- The distance on the map that represents the actual distance between City A and City B is 1.6 feet.
- The actual distance between City A and City B is 200 miles.
Now we can find the scale:
\[ \text{Scale} = \frac{\text{Actual Distance (miles)}}{\text{Map Distance (feet)}} \] \[ \text{Scale} = \frac{200 \text{ miles}}{1.6 \text{ feet}} \]
To make calculations simpler, we can convert miles to feet since there are 5280 feet in a mile:
\[ 200 \text{ miles} = 200 \times 5280 \text{ feet} = 1,056,000 \text{ feet} \]
Now substituting back into the scale formula:
\[ \text{Scale} = \frac{1,056,000 \text{ feet}}{1.6 \text{ feet}} = 660,000 \]
This scale tells us that 1 foot on the map represents 660,000 feet in real life.
Now, we need to find the actual distance between City C and City D, which are 3.2 feet apart on the map.
\[ \text{Actual Distance} = \text{Map Distance} \times \text{Scale} \] \[ \text{Actual Distance} = 3.2 \text{ feet} \times 660,000 \text{ feet/foot} = 2,112,000 \text{ feet} \]
Now, converting feet back to miles:
\[ \text{Actual Distance (miles)} = \frac{2,112,000 \text{ feet}}{5280 \text{ feet/mile}} \approx 400 \text{ miles} \]
Thus, the actual distance between City C and City D is 400 miles.
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