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Answer :
Sure! Let's go through the solution step by step for the problem about the distance between the cities Ashville, Boulder, and Wellspring on the map.
1. Understand the scale of the map:
- The map uses a scale where 0.5 inches on the map represents 15 miles in reality.
2. Distance on the map:
- The distance between Ashville and Boulder on the map is given as 2.5 inches.
3. Find the actual distance between Ashville and Boulder:
- First, divide the distance on the map by the scale's map measurement to find how many scale units it represents:
[tex]\[
\frac{2.5 \text{ inches}}{0.5 \text{ inches/unit}} = 5 \text{ units}
\][/tex]
- Then, multiply by the actual measurement for each unit to find the actual distance:
[tex]\[
5 \text{ units} \times 15 \text{ miles/unit} = 75 \text{ miles}
\][/tex]
- Therefore, the actual distance between Ashville and Boulder is 75 miles.
4. Find the distance from Wellspring to Boulder:
- Since Wellspring is exactly halfway between Ashville and Boulder, the distance from Wellspring to Boulder is half of the total distance:
[tex]\[
\frac{75 \text{ miles}}{2} = 37.5 \text{ miles}
\][/tex]
- So, the actual distance from Wellspring to Boulder is 37.5 miles.
In conclusion:
- The actual distance between Ashville and Boulder is 75 miles.
- The distance from Wellspring to Boulder is 37.5 miles.
1. Understand the scale of the map:
- The map uses a scale where 0.5 inches on the map represents 15 miles in reality.
2. Distance on the map:
- The distance between Ashville and Boulder on the map is given as 2.5 inches.
3. Find the actual distance between Ashville and Boulder:
- First, divide the distance on the map by the scale's map measurement to find how many scale units it represents:
[tex]\[
\frac{2.5 \text{ inches}}{0.5 \text{ inches/unit}} = 5 \text{ units}
\][/tex]
- Then, multiply by the actual measurement for each unit to find the actual distance:
[tex]\[
5 \text{ units} \times 15 \text{ miles/unit} = 75 \text{ miles}
\][/tex]
- Therefore, the actual distance between Ashville and Boulder is 75 miles.
4. Find the distance from Wellspring to Boulder:
- Since Wellspring is exactly halfway between Ashville and Boulder, the distance from Wellspring to Boulder is half of the total distance:
[tex]\[
\frac{75 \text{ miles}}{2} = 37.5 \text{ miles}
\][/tex]
- So, the actual distance from Wellspring to Boulder is 37.5 miles.
In conclusion:
- The actual distance between Ashville and Boulder is 75 miles.
- The distance from Wellspring to Boulder is 37.5 miles.
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