Average Speed Calculation for the Journey

To determine the average speed for the entire journey, we need to calculate the total distance covered and the total time consumed. The average speed is defined as the total distance divided by the total time.

The formula used is:

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

Calculating Time for Each Segment

The journey consists of two parts, each with a different distance and speed. We need to find the time taken for each part separately using the formula:

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

Segment 1: Distance and Speed

• Distance traveled ($d_1$) = 200 km
• Speed during this segment ($s_1$) = 50 km/hr
• Time taken for Segment 1 ($t_1$) is calculated as:

  $ t_1 = \frac{d_1}{s_1} = \frac{200 \text{ km}}{50 \text{ km/hr}} = 4 \text{ hours} $

Segment 2: Distance and Speed

• Distance traveled ($d_2$) = 300 km
• Speed during this segment ($s_2$) = 60 km/hr
• Time taken for Segment 2 ($t_2$) is calculated as:

  $ t_2 = \frac{d_2}{s_2} = \frac{300 \text{ km}}{60 \text{ km/hr}} = 5 \text{ hours} $

Calculating Total Journey Metrics

Next, we sum the distances and times from both segments to find the overall values for the journey:

• Total Distance ($D$) = $ d_1 + d_2 = 200 \text{ km} + 300 \text{ km} = 500 \text{ km} $
• Total Time ($T$) = $ t_1 + t_2 = 4 \text{ hours} + 5 \text{ hours} = 9 \text{ hours} $

Determining the Average Speed

Now, we apply the average speed formula using the calculated total distance and total time:

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

Performing the division:

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

Final Result Rounding

The question requires the answer to be rounded off to two decimal places.

Rounding $55.555...$ to two decimal places, we get $ \bf{55.56} $ km/hr.

So, the man's average speed for the entire journey is approximately 55.56 km/hr.