Answer:
The average speed of the car will be approximately 4.1667 units.
Step-by-step explanation:
To calculate the average speed of the car, you can use the formula:
Average Speed = Total Distance / Total Time
In this case, the car travels one third of the path at a speed of 50 units and two thirds of the path at a speed of 20 units. Let's assume the total distance is D units (it doesn't affect the calculation), and we'll calculate the time taken for each segment of the path.
First segment (one third of the path at 50 units speed):
Distance = (1/3) * D
Speed = 50 units
Time = Distance / Speed = ((1/3) * D) / 50
Second segment (two thirds of the path at 20 units speed):
Distance = (2/3) * D
Speed = 20 units
Time = Distance / Speed = ((2/3) * D) / 20
Total time taken:
Total Time = Time for first segment + Time for second segment
Total Time = ((1/3) * D) / 50 + ((2/3) * D) / 20
Now, plug this value of Total Time back into the formula for average speed:
Average Speed = Total Distance / Total Time
Average Speed = D / (((1/3) * D) / 50 + ((2/3) * D) / 20)
Simplify the equation:
Average Speed = 1 / (((1/3) / 50) + ((2/3) / 20))
Average Speed = 1 / ((1/150) + (2/60))
Average Speed = 1 / (1/150 + 1/30)
Average Speed = 1 / (6/150 + 30/150)
Average Speed = 1 / (36/150)
Average Speed = 150 / 36
Average Speed ≈ 4.1667 units
The average speed of the car will be approximately 4.1667 units.