Average Speed Calculation for Journey

This problem requires calculating the average speed for a journey that involves two distinct parts, each with a different distance and speed. The key formula to remember is:

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

We need to find the total distance traveled and the total time taken to complete the journey.

Journey Details Analysis

Let's break down the journey into two parts:

• Part 1: Distance = 200 km, Speed = 50 km/hr
• Part 2: Distance = 300 km, Speed = 60 km/hr

Calculating Total Distance

The total distance is the sum of the distances from both parts of the journey.

$ \text{Total Distance} = \text{Distance}_{\text{Part 1}} + \text{Distance}_{\text{Part 2}} $

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

Calculating Time for Each Part

We use the formula: $ \text{Time} = \frac{\text{Distance}}{\text{Speed}} $

• Time for Part 1:
$ \text{Time}_1 = \frac{200 \text{ km}}{50 \text{ km/hr}} = 4 \text{ hours} $
• Time for Part 2:
$ \text{Time}_2 = \frac{300 \text{ km}}{60 \text{ km/hr}} = 5 \text{ hours} $

Calculating Total Time

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

$ \text{Total Time} = \text{Time}_1 + \text{Time}_2 $

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

Calculating Average Speed

Now we can calculate the average speed using the total distance and total time.

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

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

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

Rounding the Result

The question asks for the average speed rounded to two decimal places.

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

Therefore, the average speed for the whole journey is approximately 55.56 km/hr.