Susan is driving to Mount Shasta.On her map,she is distance of 7 3/4 inches away.The scale of the map is 1/2 inch is 50 miles.
a.) how far must susan travel to reach her destination
b.) using the scale,how far is philly,pennslvania from miami florida if it is 12 1/2 inches away
C.) If a city is 3,460 miles away,how many inches would that be on the map (write it as a fraction)
a. 775
b.1250
c.60 1/5
2014
a.) To determine the actual distance Susan must travel, we can use the given scale: 1/2 inch is equal to 50 miles.
So, we can set up a proportion:
(1/2 inch) / (50 miles) = (7 3/4 inches) / (x miles)
To solve for x, we can cross-multiply:
(1/2) * x = (7 3/4) * 50
Now, convert 7 3/4 to an improper fraction:
= (31/4) * 50
= (31 * 50)/4
= 1550/4
Simplifying the fraction:
= 775/2
Now, continuing with the equation:
(1/2) * x = (775/2)
To isolate x, divide both sides by 1/2:
x = (775/2) / (1/2)
To divide by a fraction, we multiply by its reciprocal:
x = (775/2) * (2/1)
x = 775
Therefore, Susan must travel 775 miles to reach her destination.
b.) Using the same scale, we can determine the distance between Philadelphia, Pennsylvania, and Miami, Florida.
Given, 1/2 inch is equal to 50 miles.
We have the distance on the map as 12 1/2 inches. To find the actual distance, we can set up the proportion:
(1/2 inch) / (50 miles) = (12 1/2 inches) / (x miles)
Cross-multiplying:
(1/2) * x = (12 1/2) * 50
Converting 12 1/2 to an improper fraction:
= (25/2) * 50
= (25 * 50)/2
= 1250/2
Simplifying the fraction:
= 625/1
Now, completing the equation:
(1/2) * x = (625/1)
Isolating x:
x = (625/1) / (1/2)
Dividing by a fraction is equivalent to multiplying by its reciprocal:
x = (625/1) * (2/1)
x = 625 * 2
x = 1250
Therefore, Philadelphia, Pennsylvania, and Miami, Florida, are 1250 miles apart.
c.) If a city is 3,460 miles away, we can determine the distance on the map using the scale 1/2 inch is equal to 50 miles.
We can set up the proportion:
(1/2 inch) / (50 miles) = (x inches) / (3460 miles)
Cross-multiplying:
(1/2) * 3460 = x
Simplifying the calculation:
3460/2 = x
1730 = x
Therefore, a city that is 3,460 miles away would be represented by 1,730 inches on the map.
To answer these questions, we need to know the scale of the map, which is given as 1/2 inch is equal to 50 miles. Let's use this scale to find the answers.
a.) To find the distance Susan must travel to reach her destination, we need to convert the distance on the map to actual miles. Since 1/2 inch on the map corresponds to 50 miles, we can set up a proportion:
(7 3/4 inches) / (1/2 inch) = x miles / 50 miles
To solve for x, we can cross-multiply:
(7 3/4 inches) * (50 miles) = (1/2 inch) * x miles
385 inches = x miles
Therefore, Susan must travel 385 miles to reach her destination.
b.) To find the distance between Philadelphia, Pennsylvania, and Miami, Florida, using the scale, we need to apply the same process. We have a distance of 12 1/2 inches on the map. Setting up the proportion:
(12 1/2 inches) / (1/2 inch) = x miles / 50 miles
Cross-multiplying:
(12 1/2 inches) * (50 miles) = (1/2 inch) * x miles
625 inches = x miles
Thus, Philadelphia, Pennsylvania, is 625 miles away from Miami, Florida.
c.) If a city is 3,460 miles away, we can set up a proportion like before:
(unknown inches) / (1/2 inch) = 3,460 miles / 50 miles
Cross-multiplying:
(unknown inches) * (50 miles) = (1/2 inch) * 3,460 miles
50 * unknown inches = 3,460 / 2 inch-miles
unknown inches = (3,460 / 2) / 50
unknown inches = 34.6 inches
Writing it as a fraction: 34.6 inches can be expressed as 34 3/5 inches on the map.