Solving for Average Speed in a Car Journey

The average speed is calculated by dividing the total distance traveled by the total time taken. The formula is:

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

Step 1: Calculate Time for Each Segment

First, determine the time taken for each part of the journey using the formula:

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

• Segment 1: Distance = 80 km, Speed = 40 km/hr
$ \text{Time}_1 = \frac{80 \text{ km}}{40 \text{ km/hr}} = 2 \text{ hours} $
• Segment 2: Distance = 60 km, Speed = 30 km/hr
$ \text{Time}_2 = \frac{60 \text{ km}}{30 \text{ km/hr}} = 2 \text{ hours} $

Step 2: Calculate Total Distance and Total Time

Sum the distances and times from both segments:

• Total Distance:
$ \text{Total Distance} = 80 \text{ km} + 60 \text{ km} = 140 \text{ km} $
• Total Time:
$ \text{Total Time} = 2 \text{ hours} + 2 \text{ hours} = 4 \text{ hours} $

Step 3: Calculate Average Speed

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

The average speed for the entire journey is 35 km/hr.