Question

Первую половину пути до места назначения автомобиль проехал с постоянной скоростью 40 км/ч, а вторую половину - с постоянной скоростью 60 км/ч. Определите среднюю скорость на всем пути

Answer 1

Средняя скорость
vср=S/t
vср=S/(t1+t2)
Время на 1 половине пути
t1=S/2v1
Время на 2 половине пути
t2=S/2v2
Подставляем
vcp=S/(S/2v1+S/2v2)=2v1v2/(v1+v2)
vcp=2×40×60/(40+60)=48км/ч
Ответ 48 км/ч

Answer 2

Calculation of Average Speed

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

Let's assume the total distance traveled is D.

The first half of the journey was covered at a constant speed of 40 km/h, and the second half was covered at a constant speed of 60 km/h. Since both halves cover the same distance, each half covers D/2.

To find the total time taken, we can divide the distance traveled by the respective speeds:

- Time taken for the first half: (D/2) / 40 - Time taken for the second half: (D/2) / 60

Adding these two times together will give us the total time taken for the entire journey.

Now, we can calculate the average speed by dividing the total distance traveled by the total time taken.

Let's perform the calculations step by step:

1. Let's assume the total distance traveled is D. 2. The time taken for the first half is (D/2) / 40. 3. The time taken for the second half is (D/2) / 60. 4. The total time taken is the sum of the times for the first and second halves. 5. The average speed is the total distance traveled divided by the total time taken.

Calculation Steps

1. Let's assume the total distance traveled is D. 2. The time taken for the first half is (D/2) / 40. 3. The time taken for the second half is (D/2) / 60. 4. The total time taken is the sum of the times for the first and second halves: (D/2) / 40 + (D/2) / 60. 5. The average speed is the total distance traveled divided by the total time taken: D / [(D/2) / 40 + (D/2) / 60].

Answer

To find the average speed for the entire journey, we need to calculate the expression D / [(D/2) / 40 + (D/2) / 60].

Unfortunately, the value of D is not provided in the question, so we cannot calculate the exact average speed. However, we can simplify the expression using algebraic manipulation.

Let's simplify the expression:

1. Multiply the numerator and denominator by the least common multiple (LCM) of 40 and 60, which is 120: - D / [(D/2) / 40 + (D/2) / 60] - becomes D * 120 / [(D/2) * 120 / 40 + (D/2) * 120 / 60] - which simplifies to D * 120 / [3D / 2 + 2D / 2] - further simplifies to D * 120 / (5D / 2) - and finally simplifies to (D * 120 * 2) / (5D) - which further simplifies to (240D) / (5D) - and simplifies to 48.

Therefore, the average speed for the entire journey is 48 km/h.

Please note that this calculation assumes the total distance traveled is the same for both halves of the journey. If the total distance traveled is different, the average speed will vary accordingly.