Questions: A sign shows that the distance to New York is 18 miles. A traveler wants to know what this distance is in kilometers. Help the traveler by completing the parts below. (a) Let X be the unknown number of kilometers. Using the values below, create a proportion that can be used to find X. Use the conversion 1 mile = 1.6 kilometers. (b) Use the proportion from part (a) to find the distance to New York in kilometers. Do not round any computations. kilometers

A sign shows that the distance to New York is 18 miles. A traveler wants to know what this distance is in kilometers. Help the traveler by completing the parts below.
(a) Let X be the unknown number of kilometers. Using the values below, create a proportion that can be used to find X. Use the conversion 1 mile = 1.6 kilometers.
(b) Use the proportion from part (a) to find the distance to New York in kilometers. Do not round any computations.
kilometers

Transcript text: A sign shows that the distance to New York is 18 miles. A traveler wants to know what this distance is in kilometers. Help the traveler by completing the parts below. (a) Let $X$ be the unknown number of kilometers. Using the values below, create a proportion that can be used to find $X$. Use the conversion 1 mile $=1.6$ kilometers. (b) Use the proportion from part (a) to find the distance to New York in kilometers. Do not round any computations. $\square$ kilometers

Solution

Solution Steps

Step 1: Set up the proportion

Given the conversion $ 1 $ mile $ = 1.6 $ kilometers, we can set up a proportion to find the unknown number of kilometers $ X $. The proportion is: \[ \frac{1 \text{ mile}}{1.6 \text{ kilometers}} = \frac{18 \text{ miles}}{X \text{ kilometers}} \]

Step 2: Solve for $ X $

Cross-multiply to solve for $ X $: \[ 1 \cdot X = 1.6 \cdot 18 \] \[ X = 1.6 \cdot 18 \]

Step 3: Calculate the value of $ X $

Multiply $ 1.6 $ by $ 18 $: \[ X = 28.8 \]

The distance to New York in kilometers is $ 28.8 $ kilometers.