Question Find the distance represented by a 6-inch line segment on a scale drawing where 4 inches represents 25 miles.

Studdy Solution

STEP 1

Assumptions
1. The scale of the drawing is such that 4 inches represent 25 miles.
2. A line segment on the drawing measures 6 inches.

STEP 2

We need to find out how many miles are represented by 1 inch on the drawing. To do this, we divide the number of miles by the number of inches that represent those miles.
$Miles\, per\, inch = \frac{Miles\, represented}{Inches\, representing\, those\, miles}$

STEP 3

Now, plug in the given values for the miles represented and the inches representing those miles to calculate the scale in miles per inch.
$Miles\, per\, inch = \frac{25\, miles}{4\, inches}$

STEP 4

Calculate the scale in miles per inch.
$Miles\, per\, inch = \frac{25}{4} = 6.25\, miles\, per\, inch$

STEP 5

Now that we know how many miles are represented by 1 inch on the drawing, we can find out how many miles are represented by the 6-inch line segment. We do this by multiplying the length of the line segment in inches by the number of miles per inch.
$Distance\, represented = Length\, of\, line\, segment\, in\, inches \times Miles\, per\, inch$

STEP 6

Plug in the values for the length of the line segment and the miles per inch to calculate the distance represented.
$Distance\, represented = 6\, inches \times 6.25\, miles\, per\, inch$

STEP 7

Calculate the distance represented by the 6-inch line segment.
$Distance\, represented = 6 \times 6.25 = 37.5\, miles$
The 6-inch line segment on the drawing represents 37.5 miles.

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