Example Question - actual distance
Here are examples of questions we've helped users solve.
Calculating the Actual Distance Between Two Cities Using a Map Scale
<p>Let the actual distance between the two cities be \( D \) miles.</p> <p>The map scale provided is \( 1 \text{cm} = 20 \text{mi} \).</p> <p>The cities are 0.5 centimeters apart on the map.</p> <p>Using the scale, we can write the relation as follows:</p> <p>\( 1 \text{cm} \text{ on map} = 20 \text{ mi in actual distance} \)</p> <p>Hence, \( 0.5 \text{cm} \text{ on map} = 0.5 \times 20 \text{ mi in actual distance} \)</p> <p>So, \( D = 0.5 \times 20 \)</p> <p>\( D = 10 \)</p> <p>Therefore, the actual distance between the two cities is \( 10 \) miles.</p>
Calculating Actual Distance from Map Scale
<p>Let the scale factor be \( s \), where \( s \) miles in reality are represented by 1 cm on the map.</p> <p>Now let’s assume the actual distance between the two cities is \( x \) miles.</p> <p>According to the scale, we have:</p> <p>\[ \frac{x \text{ miles (actual distance)}}{3.5 \text{ cm (map distance)}} = s \frac{\text{miles}}{\text{cm}} \]</p> <p>To solve for \( x \), multiply both sides by 3.5 cm:</p> <p>\[ x = 3.5 \cdot s \]</p> <p>The problem lacks the scale factor \( s \), so we cannot proceed further without this information. Without knowing the scale of the map, we cannot convert 3.5 centimeters to the actual distance in miles.</p> <p>Therefore, we'll need additional information to provide a numerical solution.</p>
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