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A scale on a hiking map shows that 1.5 inches represents 4 miles.
What number of actual miles are represented by 6 inches on the map?
miles

A scale on a hiking map shows that $1$ . $5$ inches represents $4$ miles. $\newline$ What number of actual miles are represented by $6$ inches on the map? $\newline$ miles

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Divide decimals by whole numbers: word problems

Full solution

Q. A scale on a hiking map shows that

1

.

5

inches represents

4

miles.

\newline

What number of actual miles are represented by

6

inches on the map?

\newline

miles

Set Up Proportion: To find out how many actual miles are represented by $6$ inches on the map, we need to set up a proportion based on the scale given. The scale tells us that $1.5$ inches represents $4$ miles. We can write this as a ratio: $1.5$ inches / $4$ miles. We want to find out how many miles correspond to $6$ inches, so we set up the proportion rac{1.5 \text{ inches}}{4 \text{ miles}} = rac{6 \text{ inches}}{x \text{ miles}}, where $x$ is the number of miles we're trying to find.
Cross-Multiply: Next, we solve for $x$ by cross-multiplying. This means we multiply $1.5$ by $x$ and $4$ by $6$ , and then set the two products equal to each other: $1.5 \times x = 4 \times 6$ .
Perform Multiplication: Now we perform the multiplication on the right side of the equation: $4 \times 6 = 24$ . So our equation now is $1.5 \times x = 24$ .
Divide Equations: To solve for $x$ , we divide both sides of the equation by $1.5$ : $x = \frac{24}{1.5}$ .
Calculate Final Result: Performing the division gives us the value of $x$ : $x = \frac{24}{1.5} = 16$ . This means that $6$ inches on the map represents $16$ actual miles.

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