Calculating Average Speed for Reshma's Journey

This problem asks us to find the average speed for Reshma's entire journey, which consists of three different parts completed using different modes of transport: a bicycle, a car, and walking.

To calculate the average speed, we need to find the total distance traveled and divide it by the total time taken for the journey. The formula for average speed is:

$$ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} $$

Step-by-Step Calculation

1. Calculate Time Taken for Each Part of the Journey

We are given the distance and speed for each part. We can calculate the time taken for each part using the formula: $ \text{Time} = \frac{\text{Distance}}{\text{Speed}} $.

• Bicycle Journey:
  • Distance = 45 km
  • Speed = 15 km/h
  • Time (Bicycle) = $ \frac{45 \text{ km}}{15 \text{ km/h}} = 3 \text{ hours} $
• Car Journey:
  • Distance = 80 km
  • Speed = 40 km/h
  • Time (Car) = $ \frac{80 \text{ km}}{40 \text{ km/h}} = 2 \text{ hours} $
• Walking Journey:
  • Distance = 6 km
  • Speed = 2 km/h
  • Time (Walking) = $ \frac{6 \text{ km}}{2 \text{ km/h}} = 3 \text{ hours} $

2. Calculate Total Distance Traveled

The total distance is the sum of the distances covered in each part of the journey.

Total Distance = Distance (Bicycle) + Distance (Car) + Distance (Walking)

Total Distance = $ 45 \text{ km} + 80 \text{ km} + 6 \text{ km} = 131 \text{ km} $

3. Calculate Total Time Taken

The total time is the sum of the times taken for each part of the journey.

Total Time = Time (Bicycle) + Time (Car) + Time (Walking)

Total Time = $ 3 \text{ hours} + 2 \text{ hours} + 3 \text{ hours} = 8 \text{ hours} $

4. Calculate the Average Speed

Now we can use the formula for average speed with the total distance and total time calculated.

$$ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{131 \text{ km}}{8 \text{ hours}} $$

$$ \text{Average Speed} = 16.375 \text{ km/h} $$

5. Round the Average Speed

The question asks for the average speed correct to 2 decimal places. Rounding 16.375 to two decimal places gives 16.38.

Average Speed $ \approx 16.38 \text{ km/h} $

Conclusion

Reshma's average speed for the whole journey is approximately 16.38 km/h.