Understanding Average Speed Calculation

This problem requires calculating the overall average speed for a journey that consists of two parts, each with a different distance and speed. The average speed is not simply the average of the two speeds; instead, it's calculated by dividing the total distance traveled by the total time taken.

Formulating the Calculation

The formula for average speed is:

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

To find the average speed, we first need to calculate the time taken for each part of the journey.

Step-by-Step Calculation

1. Calculate time for the first part:

   Distance = 200 km

   Speed = 50 km/hr

   Using the formula $ \text{Time} = \frac{\text{Distance}}{\text{Speed}} $, we get:

   $ \text{Time}_1 = \frac{200 \text{ km}}{50 \text{ km/hr}} = 4 \text{ hours} $

2. Calculate time for the second part:

   Distance = 300 km

   Speed = 60 km/hr

   Using the same formula:

   $ \text{Time}_2 = \frac{300 \text{ km}}{60 \text{ km/hr}} = 5 \text{ hours} $

3. Calculate the total distance:

   $ \text{Total Distance} = \text{Distance}_1 + \text{Distance}_2 = 200 \text{ km} + 300 \text{ km} = 500 \text{ km} $

4. Calculate the total time:

   $ \text{Total Time} = \text{Time}_1 + \text{Time}_2 = 4 \text{ hours} + 5 \text{ hours} = 9 \text{ hours} $

5. Calculate the average speed:

   Now, we apply the average speed formula:

   $ \text{Average Speed} = \frac{500 \text{ km}}{9 \text{ hours}} $

   $ \text{Average Speed} \approx 55.555... \text{ km/hr} $

6. Round the result:

   The question asks to round the answer to two decimal places.

   $ \text{Average Speed} \approx 55.56 \text{ km/hr} $

Final Answer

The average speed for the whole journey, rounded to two decimal places, is 55.56 km/hr.