Question
Use the information to answer the question.
On a map, the distance from the park entrance to the beach is 8.5 centimeters. The map uses a scale of 1: 50,000. Myra plans to run from the park entrance to the beach at a speed of 10 kilometers per hour.
How many minutes will it take Myra to run from the park entrance to the beach? Enter the answer in the box.
On a map, the distance from the park entrance to the beach is 8.5 centimeters. The map uses a scale of 1: 50,000. Myra plans to run from the park entrance to the beach at a speed of 10 kilometers per hour.
How many minutes will it take Myra to run from the park entrance to the beach? Enter the answer in the box.
Answers
GPT-4o mini
To determine how many minutes it will take Myra to run from the park entrance to the beach, we first need to convert the distance on the map to the actual distance in kilometers.
**Step 1: Convert the map distance to actual distance.**
The map distance from the park entrance to the beach is 8.5 centimeters. The scale of the map is 1:50,000, which means 1 cm on the map represents 50,000 cm in reality.
To convert the map distance to actual distance:
\[
\text{Actual distance (in cm)} = 8.5 \, \text{cm} \times 50,000 = 425,000 \, \text{cm}
\]
Now, convert centimeters to kilometers:
\[
\text{Actual distance (in km)} = \frac{425,000 \, \text{cm}}{100,000 \, \text{cm/km}} = 4.25 \, \text{km}
\]
**Step 2: Calculate the time taken to run this distance.**
Myra's speed is 10 kilometers per hour. To find the time it takes to run 4.25 kilometers, we can use the formula:
\[
\text{Time (in hours)} = \frac{\text{Distance (in km)}}{\text{Speed (in km/h)}}
\]
Substituting the values, we have:
\[
\text{Time (in hours)} = \frac{4.25 \, \text{km}}{10 \, \text{km/h}} = 0.425 \, \text{hours}
\]
**Step 3: Convert time from hours to minutes.**
To convert hours into minutes, multiply by 60:
\[
\text{Time (in minutes)} = 0.425 \, \text{hours} \times 60 \, \text{minutes/hour} = 25.5 \, \text{minutes}
\]
**Final Answer:**
It will take Myra approximately **25.5 minutes** to run from the park entrance to the beach.
**Step 1: Convert the map distance to actual distance.**
The map distance from the park entrance to the beach is 8.5 centimeters. The scale of the map is 1:50,000, which means 1 cm on the map represents 50,000 cm in reality.
To convert the map distance to actual distance:
\[
\text{Actual distance (in cm)} = 8.5 \, \text{cm} \times 50,000 = 425,000 \, \text{cm}
\]
Now, convert centimeters to kilometers:
\[
\text{Actual distance (in km)} = \frac{425,000 \, \text{cm}}{100,000 \, \text{cm/km}} = 4.25 \, \text{km}
\]
**Step 2: Calculate the time taken to run this distance.**
Myra's speed is 10 kilometers per hour. To find the time it takes to run 4.25 kilometers, we can use the formula:
\[
\text{Time (in hours)} = \frac{\text{Distance (in km)}}{\text{Speed (in km/h)}}
\]
Substituting the values, we have:
\[
\text{Time (in hours)} = \frac{4.25 \, \text{km}}{10 \, \text{km/h}} = 0.425 \, \text{hours}
\]
**Step 3: Convert time from hours to minutes.**
To convert hours into minutes, multiply by 60:
\[
\text{Time (in minutes)} = 0.425 \, \text{hours} \times 60 \, \text{minutes/hour} = 25.5 \, \text{minutes}
\]
**Final Answer:**
It will take Myra approximately **25.5 minutes** to run from the park entrance to the beach.