The distance between two towns is 120 kilometers. There are approximately 8 kilometers in 5 miles. Which measurement is closest to the number of miles between these towns?

Steps to Solve

1. Determine the conversion factor We know that there are approximately 8 kilometers in 5 miles. To find out how many kilometers are in 1 mile, we can set up the following ratio:

$$ \text{Kilometers per mile} = \frac{8 \text{ kilometers}}{5 \text{ miles}} $$

From this, we can find:

$$ 1 \text{ mile} = \frac{8}{5} \text{ kilometers} $$

2. Convert kilometers to miles Next, we want to convert 120 kilometers into miles. We can use the conversion we derived in the previous step. To find the number of miles ($m$) for 120 kilometers ($k$), we can rearrange the formula:

$$ m = \frac{k}{\text{Kilometers per mile}} $$

Substituting our values:

$$ m = \frac{120 \text{ kilometers}}{\frac{8}{5} \text{ kilometers per mile}} $$

3. Calculate the miles To simplify the calculation, multiply 120 by the reciprocal of $\frac{8}{5}$:

$$ m = 120 \times \frac{5}{8} $$

Calculating this gives:

$$ m = 120 \times 0.625 $$

4. Final calculation Now we compute the final value:

$$ m = 75 \text{ miles} $$