Question

2/3 пути автомобилист проехал со скоростью 50 км/ч,а 1/3 со скоростью 120 км/ч. Найти среднюю скорость?

Answer 1

1) найти весь пройденный путь;

2) найти все время движения;

3) весь пройденный путь разделить на все время движения:

Answer 2

To find the average speed, we can use the formula:

Average speed = Total distance / Total time

Let's assume the total distance is D kilometers. Since the motorist travels 2/3 of the distance at 50 km/h and 1/3 of the distance at 120 km/h, we can calculate the distances covered at each speed.

Distance at 50 km/h = (2/3) * D Distance at 120 km/h = (1/3) * D

Now, let's find the time taken for each segment of the journey:

Time at 50 km/h = Distance at 50 km/h / Speed at 50 km/h Time at 50 km/h = ((2/3) * D) / 50

Time at 120 km/h = Distance at 120 km/h / Speed at 120 km/h Time at 120 km/h = ((1/3) * D) / 120

Now, to find the total time of the journey, we add the times taken at each speed:

Total time = Time at 50 km/h + Time at 120 km/h Total time = ((2/3) * D) / 50 + ((1/3) * D) / 120

Next, we find the average speed using the formula:

Average speed = Total distance / Total time Average speed = D / ( ((2/3) * D) / 50 + ((1/3) * D) / 120 )

Now, we can simplify the equation:

Average speed = 1 / ( ((2/3) / 50) + ((1/3) / 120) )

To get the final answer, let's calculate the average speed:

Average speed ≈ 1 / ( (2/3) * (1/50) + (1/3) * (1/120) ) Average speed ≈ 1 / (1/75 + 1/3600) Average speed ≈ 1 / (48/3600 + 5/3600) Average speed ≈ 1 / (53/3600) Average speed ≈ 3600/53 ≈ 67.9245 km/h

The average speed of the motorist for the whole journey is approximately 67.92 km/h.