QuestionThe map's scale is 1 inch = 16 miles. If the distance is $2 \frac{3}{4}$ inches, how many miles apart are the cities?

Studdy Solution

STEP 1

Assumptions1. The scale of the map is1 inch equals16 miles. . The distance on the map between the two cities is $\frac{3}{4}$ inches.

STEP 2

We need to convert the distance on the map to the actual distance. We can do this by multiplying the distance on the map by the scale of the map.
$Actual\, distance = Distance\, on\, map \\times Scale\, of\, map$

STEP 3

Now, plug in the given values for the distance on the map and the scale of the map to calculate the actual distance.
$Actual\, distance =2 \frac{3}{} \, inches \\times16\, miles/inch$

STEP 4

First, convert the mixed fraction to an improper fraction.
$2 \frac{3}{4} = \frac{11}{4}$ $Actual\, distance = \frac{11}{4} \, inches \\times16\, miles/inch$

STEP 5

Calculate the actual distance.
$Actual\, distance = \frac{11}{4} \, inches \\times16\, miles/inch =44\, miles$ The cities are44 miles apart.

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