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:
$ \text{Average Speed} = \frac{140 \text{ km}}{4 \text{ hours}} = 35 \text{ km/hr} $
The average speed for the entire journey is 35 km/hr.