A car travels for 30 minutes at a speed of 50 km/h, the next 40 minutes at a…

To find the distance traveled in the final segment, we first need to determine the total distance of the journey and subtract the distances covered in the first two segments.

Calculate the Total Time:
Total time = 30 minutes + 40 minutes + 50 minutes = 120 minutes.
Convert 120 minutes to hours: 120 / 60 = 2 hours.

Calculate the Total Distance:
We know the average speed for the whole journey is 42 km/h.
Total Distance = Average Speed × Total Time
Total Distance = 42 km/h × 2 hours = 84 km.

Calculate the Distance of the First Segment (D1):
Time = 30 minutes = 30/60 hours = 1/2 hour.
Speed = 50 km/h.
D1 = Speed × Time = 50 × 1/2 = 25 km.

Calculate the Distance of the Second Segment (D2):
Time = 40 minutes = 40/60 hours = 2/3 hour.
Speed = 40 km/h.
D2 = Speed × Time = 40 × 2/3 = 80/3 km.

Calculate the Distance of the Third Segment (D3):
D3 represents the distance traveled at x km/h.
Total Distance = D1 + D2 + D3
84 = 25 + 80/3 + D3
D3 = 84 - 25 - 80/3
D3 = 59 - 80/3
Make the denominators equal to subtract:
D3 = (177 - 80) / 3
D3 = 97 / 3 km.

Convert to Mixed Fraction:
97 ÷ 3 = 32 with a remainder of 1.
Therefore, D3 = 32 1/3 km.