Omaha, Nebraska, and Sioux City, Iowa, are 90 miles apart. If the distance on the map is 1 1/2 inches, find the scale of the map.
1 inches is equal to 90 miles
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To find the scale of the map, we need to determine the ratio between the actual distance on the ground and the distance on the map. In this case, we know that Omaha, Nebraska, and Sioux City, Iowa, are 90 miles apart in reality, and the distance on the map is given as 1 1/2 inches.
To calculate the scale, we divide the actual distance by the map distance:
Scale = Actual Distance / Map Distance
Scale = 90 miles / 1 1/2 inches
First, we need to convert the mixed number, 1 1/2, to an improper fraction. To do this, we multiply the whole number (1) by the denominator (2) and add the result (2) to the numerator (1). This gives us:
Scale = 90 miles / (3/2) inches
To divide by a fraction, we can multiply by its reciprocal:
Scale = 90 miles * (2/3) inches/mile
Now, we can simplify the calculation:
Scale = (90 * 2) / (3 * 1)
Scale = 180 / 3
Scale = 60
Therefore, the scale of the map is 1 inch on the map represents 60 miles on the ground.
90 / 1.5 = 60
1 inch - 90 miles