Sarah's mother has a miniature village modeled after her hometown. The model is 10 ft long and 7ft wide. the actual village is 7 miles long. what is the villages actual width? if necessary round to the nearest tenth of a mile.
10 ft / 7 mi = 7 ft / w
10 / 7 = 7 / w
10 w = 7 * 7
10 w = 49
w = 49 / 10 = 4.9
w = 4.9 mi
To find the actual width of the village, we can use the concept of scales. The scale is the ratio between the model and the actual object. In this case, we know that the model is 10 ft long and 7 ft wide, while the actual village is 7 miles long.
First, let's determine the scale for the length of the model village:
Model length / Actual length = Scale length
10 ft / 7 miles = Scale length
To find the actual width, we need to use the same scale since both the length and width of the model village are proportional to the actual village.
Actual width = Scale length x Model width
Let's plug in the values:
Scale length = 10 ft / 7 miles
Model width = 7 ft
Actual width = (10 ft / 7 miles) * 7 ft
Now, let's convert the units to have a uniform measurement:
Actual width = (10 ft / 7 miles) * (5280 ft / 1 mile) * 7 ft
Simplifying the expression:
Actual width = 10 ft * 5280 ft / (7 miles * 1 mile) * 7 ft
Actual width = (10 * 5280) ft² / (7 * 1) miles
Calculating:
Actual width = 52800 ft² / 7 miles
Actual width ≈ 7542.9 ft²/mile
Rounding to the nearest tenth of a mile:
Actual width ≈ 7542.9 ft²/mile ≈ 7542.9 / 5280 ≈ 1.43 miles
Therefore, the village's actual width is approximately 1.4 miles.