To find the average speed for the entire journey, we need to calculate the total distance covered and the total time taken.

Calculating Time for Each Segment

The journey is divided into three equal segments of 160 km each.

• Segment 1: Distance = 160 km, Speed = 80 km/hr. Time taken (\(t_1\)) = \(\frac{\text{Distance}}{\text{Speed}} = \frac{160 \text{ km}}{80 \text{ km/hr}} = 2 \text{ hours}\).
• Segment 2: Distance = 160 km, Speed = 120 km/hr. Time taken (\(t_2\)) = \(\frac{\text{Distance}}{\text{Speed}} = \frac{160 \text{ km}}{120 \text{ km/hr}} = \frac{4}{3} \text{ hours}\).
• Segment 3: Distance = 160 km, Speed = 80 km/hr. Time taken (\(t_3\)) = \(\frac{\text{Distance}}{\text{Speed}} = \frac{160 \text{ km}}{80 \text{ km/hr}} = 2 \text{ hours}\).

Calculating Total Distance and Total Time

• Total Distance: The racer car covers 160 km in each of the three segments. Total Distance = \(160 \text{ km} + 160 \text{ km} + 160 \text{ km} = 480 \text{ km}\).
• Total Time: Sum the time taken for each segment. Total Time = \(t_1 + t_2 + t_3 = 2 \text{ hours} + \frac{4}{3} \text{ hours} + 2 \text{ hours}\). Total Time = \(4 + \frac{4}{3} = \frac{12}{3} + \frac{4}{3} = \frac{16}{3} \text{ hours}\).

Calculating Average Speed

The formula for average speed is Total Distance divided by Total Time.

Average Speed = \(\frac{\text{Total Distance}}{\text{Total Time}}\)

Average Speed = \(\frac{480 \text{ km}}{\frac{16}{3} \text{ hours}} = \frac{480 \times 3}{16} \text{ km/hr}\)

Average Speed = \(30 \times 3 \text{ km/hr} = 90 \text{ km/hr}\).

Therefore, the average speed of the racer car for the entire journey is 90 km/hr.