Math Problem Statement

Ajay walked at an average speed of 8 km/h for 45 minutes and then ran at an average speed of 12 km/h for 40 minutes. What was his average speed for the whole journey?

Solution

Let's solve the question from the image:

Problem: Ajay walked at an average speed of 8 km/h for 45 minutes and then ran at an average speed of 12 km/h for 40 minutes. What was his average speed for the whole journey?

Step 1: Convert time into hours

  • Walking: 45minutes=4560=0.75hours45 \, \text{minutes} = \frac{45}{60} = 0.75 \, \text{hours}
  • Running: 40minutes=4060=0.6667hours40 \, \text{minutes} = \frac{40}{60} = 0.6667 \, \text{hours}

Step 2: Calculate the distances

  • Distance walked = Speed × Time = 8km/h×0.75hours=6km8 \, \text{km/h} \times 0.75 \, \text{hours} = 6 \, \text{km}
  • Distance ran = Speed × Time = 12km/h×0.6667hours=8km12 \, \text{km/h} \times 0.6667 \, \text{hours} = 8 \, \text{km}

Step 3: Total distance and total time

  • Total distance = 6km+8km=14km6 \, \text{km} + 8 \, \text{km} = 14 \, \text{km}
  • Total time = 0.75hours+0.6667hours=1.4167hours0.75 \, \text{hours} + 0.6667 \, \text{hours} = 1.4167 \, \text{hours}

Step 4: Average speed formula

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

Average speed=14km1.4167hours9.88km/h\text{Average speed} = \frac{14 \, \text{km}}{1.4167 \, \text{hours}} \approx 9.88 \, \text{km/h}

Final Answer:

Ajay's average speed for the whole journey is approximately 9.88 km/h.

Would you like more details or have any further questions?


Here are 5 related questions to expand on this topic:

  1. How would the average speed change if Ajay ran for 50 minutes instead of 40 minutes?
  2. What is the significance of average speed compared to instantaneous speed in this context?
  3. Can you calculate the average speed if both walking and running times are equal?
  4. How does the formula for average speed differ for equal and unequal time intervals?
  5. How can you determine average velocity if direction is involved?

Tip: When working with speed problems, always convert time units to hours for consistency in calculations!

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Math Problem Analysis

Mathematical Concepts

Average speed
Unit conversion
Time and distance calculations

Formulas

Distance = Speed × Time
Average speed = Total distance / Total time

Theorems

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Suitable Grade Level

Grades 6-8