The problem asks for the average speed of a car over a multi-segment journey, including a stoppage time. Average speed is calculated as Total Distance divided by Total Time.

Calculating Total Distance

The total distance is the sum of the distances covered in each segment:

• Segment 1: 120 km
• Segment 2: 200 km
• Segment 3: 150 km

Total Distance = \(120 \text{ km} + 200 \text{ km} + 150 \text{ km} = 470 \text{ km}\)

Calculating Total Time

First, calculate the time taken for each segment using the formula: Time = Distance / Speed.

• Segment 1 Time:

  Time = \(\frac{120 \text{ km}}{60 \text{ km/h}} = 2 \text{ hours}\)

• Segment 2 Time:

  Time = \(\frac{200 \text{ km}}{80 \text{ km/h}} = 2.5 \text{ hours}\)

• Segment 3 Time:

  Time = \(\frac{150 \text{ km}}{100 \text{ km/h}} = 1.5 \text{ hours}\)

Next, account for the stoppage time during the second segment. Convert minutes to hours:

Stoppage Time = \(20 \text{ minutes} = \frac{20}{60} \text{ hours} = \frac{1}{3} \text{ hours}\)

Now, sum all the times to find the total duration of the journey:

Total Time = (Segment 1 Time) + (Segment 2 Time) + (Segment 3 Time) + (Stoppage Time)

Total Time = \(2 \text{ hours} + 2.5 \text{ hours} + 1.5 \text{ hours} + \frac{1}{3} \text{ hours}\)

Total Time = \(6 \text{ hours} + \frac{1}{3} \text{ hours} = \frac{18}{3} \text{ hours} + \frac{1}{3} \text{ hours} = \frac{19}{3} \text{ hours}\)

Calculating Average Speed

Use the formula for average speed:

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

Average Speed = \(\frac{470 \text{ km}}{\frac{19}{3} \text{ hours}}\)

Average Speed = \(\frac{470 \times 3}{19} \text{ km/h}\)

Average Speed = \(\frac{1410}{19} \text{ km/h}\)

Average Speed \(\approx 74.2105... \text{ km/h}\)

Rounding to one decimal place, the average speed is 74.2 km/h.