Math Problem Statement

Mia is walking around the city park. Then she decided to run that same distance. Her walking speed is 4 mph and her running speed is 8 mph. If it took her 3 hours to walk around the park, how much time did it take her to run around the park?

Solution

The problem in the image is:

Mia is walking around the city park. Then she decided to run that same distance. Her walking speed is 4 mph and her running speed is 8 mph. If it took her 3 hours to walk around the park, how much time did it take her to run around the park?

Solution:

First, let's calculate the distance Mia walked around the park. Since distance is calculated using the formula:

Distance=Speed×Time\text{Distance} = \text{Speed} \times \text{Time}

Given her walking speed is 4 mph and the time spent walking is 3 hours, the distance she walked is:

Distance=4mph×3hours=12miles\text{Distance} = 4 \, \text{mph} \times 3 \, \text{hours} = 12 \, \text{miles}

Now, she runs the same distance, but at a speed of 8 mph. To find out how much time it took her to run, we use the formula:

Time=DistanceSpeed\text{Time} = \frac{\text{Distance}}{\text{Speed}}

Substituting the values:

Time=12miles8mph=1.5hours\text{Time} = \frac{12 \, \text{miles}}{8 \, \text{mph}} = 1.5 \, \text{hours}

Answer:

It took Mia 1.5 hours to run around the park.


Do you have any questions or would you like more details?

Here are 5 related questions to consider:

  1. How would the answer change if Mia's running speed was 10 mph instead of 8 mph?
  2. What is the total time Mia spent for both walking and running the park?
  3. If Mia walked half the distance and ran the other half, how long would the entire journey take?
  4. How long would it take Mia to walk twice the distance at the same speed?
  5. What is the ratio of her walking time to her running time?

Tip: When working with distance, time, and speed, always ensure the units are consistent throughout the calculations.

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Math Problem Analysis

Mathematical Concepts

Distance
Time
Speed
Proportions

Formulas

Distance = Speed × Time
Time = Distance / Speed

Theorems

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Suitable Grade Level

Grades 5-7