If a road map has a scale of 3 in. : 100 mi., find the following distances. 23. How far is it between Cardwell and Claremont if they are 4.5 in. apart on the map? 24. How far is it between Kingston and Goldsboro if they are 2 in. apart? Round to the nearest mile. 25. If Dodge City and Pine Bluff are 500 mi. apart, what is the distance between them on a map? 26. If Stenson and South Fork are 175 mi. apart, what is the distance between them on the map? SHOW WORK
23. To find the actual distance between Cardwell and Claremont, we can set up a proportion using the scale of the map:
3 in. : 100 mi. = 4.5 in. : x
Cross-multiplying and solving for x, we get:
x = (4.5 in. * 100 mi.) / 3 in. = 150 miles
Therefore, it is 150 miles between Cardwell and Claremont.
24. Similarly, to find the actual distance between Kingston and Goldsboro, we set up a proportion using the scale of the map:
3 in. : 100 mi. = 2 in. : x
Cross-multiplying and solving for x, we get:
x = (2 in. * 100 mi.) / 3 in. ≈ 67 miles
Therefore, it is approximately 67 miles between Kingston and Goldsboro.
25. To find the distance between Dodge City and Pine Bluff on the map, we need to use the inverse of the scale:
100 mi. : 3 in. = x mi. : 1 in.
Cross-multiplying and solving for x, we get:
x = (100 mi. * 1 in.) / 3 in. ≈ 33.33 miles/in.
To find the distance on the map, we can multiply the actual distance by the scale:
x = 500 mi. * 1 in. / 33.33 miles/in. ≈ 15 in.
Therefore, the distance between Dodge City and Pine Bluff on the map is approximately 15 inches.
26. Again, using the inverse of the scale, we set up a proportion:
100 mi. : 3 in. = 175 mi. : x in.
Cross-multiplying and solving for x, we get:
x = (175 mi. * 3 in.) / 100 mi. = 5.25 in.
Therefore, the distance between Stenson and South Fork on the map is 5.25 inches.
To solve these questions, we'll use the scale provided on the road map, which is 3 in. : 100 mi.
23. To find the actual distance between Cardwell and Claremont, we'll use the given measurement on the map, which is 4.5 in. We can set up a ratio where the distance on the map is in proportion to the actual distance:
(3 in. / 100 mi.) = (4.5 in. / x mi.)
To solve for x, we cross-multiply and then divide:
3 * x = 100 * 4.5
3x = 450
x = 450 / 3
x = 150 mi.
So, the actual distance between Cardwell and Claremont is 150 miles.
24. Following the same steps, for the distance between Kingston and Goldsboro (2 in.), the calculation will be:
(3 in. / 100 mi.) = (2 in. / x mi.)
3 * x = 100 * 2
3x = 200
x = 200 / 3
x ≈ 66.67 mi.
Rounding to the nearest mile, the actual distance between Kingston and Goldsboro is approximately 67 miles.
25. In this scenario, the actual distance between Dodge City and Pine Bluff is provided (500 mi.). To find the distance on the map, we'll set up a proportion:
(3 in. / 100 mi.) = (x in. / 500 mi.)
3 * 500 = 100 * x
1500 = 100x
x = 1500 / 100
x = 15 in.
Therefore, the distance between Dodge City and Pine Bluff on the map is 15 inches.
26. Similarly, for the distance between Stenson and South Fork (175 mi.), the calculation is:
(3 in. / 100 mi.) = (x in. / 175 mi.)
3 * 175 = 100 * x
525 = 100x
x = 525 / 100
x = 5.25 in.
Hence, the distance between Stenson and South Fork on the map is 5.25 inches.
To summarize:
- The actual distance between Cardwell and Claremont is 150 miles.
- The actual distance between Kingston and Goldsboro is approximately 67 miles.
- The distance between Dodge City and Pine Bluff on the map is 15 inches.
- The distance between Stenson and South Fork on the map is 5.25 inches.
To find the distances using the given scale, you can set up proportions between the distances on the map and the actual distances.
23. Distance between Cardwell and Claremont:
Let x be the actual distance between Cardwell and Claremont.
According to the scale, 3 in. on the map represents 100 mi.
Therefore, we can set up the proportion: 3 in. / 100 mi. = 4.5 in. / x
Cross-multiplying, we get: 3 in. * x = 100 mi. * 4.5 in.
3x = 450 mi
x = 450 mi / 3
x = 150 mi
So, the actual distance between Cardwell and Claremont is 150 miles.
24. Distance between Kingston and Goldsboro:
Let y be the actual distance between Kingston and Goldsboro.
According to the scale, 3 in. on the map represents 100 mi.
Therefore, we can set up the proportion: 3 in. / 100 mi. = 2 in. / y
Cross-multiplying, we get: 3 in. * y = 100 mi. * 2 in.
3y = 200 mi
y = 200 mi / 3
y ≈ 66.67 mi (rounded to the nearest mile)
So, the actual distance between Kingston and Goldsboro is approximately 67 miles.
25. Distance on the map between Dodge City and Pine Bluff:
Let d be the distance on the map between Dodge City and Pine Bluff.
According to the scale, 3 in. on the map represents 100 mi.
Therefore, we can set up the proportion: 3 in. / 100 mi. = d / 500 mi.
Cross-multiplying, we get: 3 in. * 500 mi. = 100 mi. * d
1500 = 100d
d = 1500 / 100
d = 15 in.
So, the distance between Dodge City and Pine Bluff on the map is 15 inches.
26. Distance on the map between Stenson and South Fork:
Let s be the distance on the map between Stenson and South Fork.
According to the scale, 3 in. on the map represents 100 mi.
Therefore, we can set up the proportion: 3 in. / 100 mi. = s / 175 mi.
Cross-multiplying, we get: 3 in. * 175 mi. = 100 mi. * s
525 = 100s
s = 525 / 100
s = 5.25 in.
So, the distance between Stenson and South Fork on the map is 5.25 inches.