Math Problem Statement

A group of friends is taking part in a two-day walking event for charity. Yesterday, they walked 28 miles in 9 hours and 44 minutes. Today, they finished the last 10 miles in 2 hours and 55 minutes. What was the group's average speed for the two-day event? Write your answer as a whole number or as a decimal rounded to the nearest tenth. miles per hour

Solution

To find the group's average speed for the entire two-day walking event, we first need to calculate the total distance walked and the total time taken, then divide the total distance by the total time.

Step 1: Calculate the total distance

  • Distance walked on the first day: 28 miles
  • Distance walked on the second day: 10 miles
  • Total distance = 28 miles + 10 miles = 38 miles

Step 2: Calculate the total time

  • Time spent walking on the first day: 9 hours and 44 minutes

    • Convert 44 minutes to hours: 44÷60=0.733344 \div 60 = 0.7333 hours
    • Total time for the first day = 9 + 0.7333 = 9.7333 hours
  • Time spent walking on the second day: 2 hours and 55 minutes

    • Convert 55 minutes to hours: 55÷60=0.916755 \div 60 = 0.9167 hours
    • Total time for the second day = 2 + 0.9167 = 2.9167 hours
  • Total time = 9.7333 hours + 2.9167 hours = 12.65 hours

Step 3: Calculate the average speed

Average speed = Total distanceTotal time\frac{\text{Total distance}}{\text{Total time}}

Average speed=38 miles12.65 hours3.0 miles per hour\text{Average speed} = \frac{38 \text{ miles}}{12.65 \text{ hours}} \approx 3.0 \text{ miles per hour}

Thus, the group's average speed for the two-day event is approximately 3.0 miles per hour.

Would you like more details or have any questions on this? Here are some related questions to explore:

  1. How do you convert minutes to hours for different times?
  2. What is the formula for average speed?
  3. How can you calculate the total distance and time when walking multiple days?
  4. What is the effect of different walking speeds on average speed calculations?
  5. How would the average speed change if the group walked a longer distance?

Tip: When converting minutes to hours, always divide the number of minutes by 60 to get a decimal value.

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Math Problem Analysis

Mathematical Concepts

Average Speed
Distance and Time Calculations
Unit Conversion (Minutes to Hours)

Formulas

Average Speed = Total Distance / Total Time

Theorems

Basic properties of average speed

Suitable Grade Level

Grades 7-9