On a map, 1 centimeter represents 7½cm kilometers. What length On the map would represent a distance of 45 kilometers?

Question

On a map, 1 centimeter represents 7½cm kilometers. What length On the map would represent a distance of 45 kilometers?

Answer 1

To find the length on the map that represents a distance of 45 kilometers, we need to use the given scale of 1 centimeter representing 7½ kilometers.

First, we need to determine how many centimeters equal 1 kilometer:

1 centimeter represents 7½ kilometers

Therefore, 1 kilometer represents 1/(7½) = 2/15 centimeters.

Next, we can calculate the length on the map that represents 45 kilometers:

45 kilometers represents (45 * 2/15) = 6 centimeters.

Therefore, a length of 6 centimeters on the map would represent a distance of 45 kilometers.

Answer 2

To determine the length on the map that represents a distance of 45 kilometers, we need to use the given scale. The scale states that 1 centimeter on the map represents 7½ kilometers.

We can set up a proportion to solve for the unknown length on the map:

1 cm / 7½ km = x cm / 45 km

To solve for x, we can cross-multiply:

7½ km * x cm = 1 cm * 45 km

We can simplify:

7½x = 45

Now, divide both sides by 7½:

x = 45 / 7½

To simplify further, we can convert 7½ to an improper fraction:

7½ = 7 + ½ = 15/2

Now, substitute 15/2 for 7½:

x = 45 / (15/2)

To divide by a fraction, we multiply by its reciprocal:

x = 45 * (2/15)

Simplifying the multiplication:

x = 6 cm

Therefore, a length of 6 centimeters on the map would represent a distance of 45 kilometers.

Answer 3

To find out the length on the map that represents a distance of 45 kilometers, we need to use the scale given in the question. The scale on the map states that 1 centimeter represents 7½ kilometers.

First, we determine the ratio between the distance on the map and the actual distance:

1 centimeter represents 7½ kilometers.

To simplify the calculation, let's convert 7½ kilometers into a decimal:

7½ kilometers = 7.5 kilometers.

Now we have:

1 centimeter represents 7.5 kilometers.

Next, we need to find the length on the map that represents 45 kilometers. We can set up a proportion to solve for this value:

1 centimeter is to 7.5 kilometers as X centimeters is to 45 kilometers.

Using cross-multiplication, we get:

1 * 45 = 7.5 * X.

Simplifying this equation, we find:

45 = 7.5X.

To solve for X, we divide both sides of the equation by 7.5:

X = 45 / 7.5.

Evaluating this equation, we get:

X = 6.

Therefore, on the map, a length of 6 centimeters would represent a distance of 45 kilometers.