Question

Помогите пожалуйста!!!Такси проехало 2/3 пути со скоростью 50 км / ч, а остальные с такой скоростью, что средняя скорость на всем пути равна 37,5 км / ч. Вычислить скорость движения такси на последней трети пути.

Answer 1

Такси проехало 2/3 пути со скоростью 50 км / ч, а остальные с такой скоростью, что средняя скорость на всем пути равна 37,5 км / ч. Вычислить скорость движения такси на последней трети пути.
Дано  S1=2*S/3 V1=50 км/ч S2=S/3  Vср=37,5 км/ч   V2-?

Vср=S/(t1+t2)
t1+t2=2*S/3*V1+S/3*V2=S/3   * (2/V1 +1/V2)

Vср=3/(2/V1+1/V2)
Vср=3*V1*V2/(2*V2+V1)
Vcр*2*V2 +Vср*V1=3*V1*V2

V2=Vcр*V1/(3*V1 - 2*Vср)=37,5*50/(150-75)=25 км/ч

Ответ V2=25 км/ч

Проверка ( это писать не надо) 
пусть S=150 км   S1=100   S2=50
t1=S1/V1=2     t2=50/25=2
t=4
Vср=150/4=37,5 км/ч
Значит Я решила верно.

Answer 2

Problem Analysis

We are given that a taxi traveled 2/3 of the distance at a speed of 50 km/h, and the remaining distance at an unknown speed. The average speed for the entire journey is given as 37.5 km/h. We need to calculate the speed of the taxi for the last third of the journey.

Solution

Let's assume the total distance traveled by the taxi is D km.

We know that the taxi traveled 2/3 of the distance at a speed of 50 km/h. This means it traveled (2/3) * D km at 50 km/h.

The remaining distance, which is 1/3 of the total distance, is (1/3) * D km.

We are given that the average speed for the entire journey is 37.5 km/h. We can use the formula for average speed:

Average speed = Total distance / Total time

We can rearrange this formula to find the total time:

Total time = Total distance / Average speed

For the first 2/3 of the distance, the time taken is:

Time taken for the first 2/3 of the distance = (2/3) * D / 50

For the last 1/3 of the distance, the time taken is:

Time taken for the last 1/3 of the distance = (1/3) * D / x, where x is the speed for the last third of the journey.

Since the average speed for the entire journey is given as 37.5 km/h, we can set up the equation:

Total time = Time taken for the first 2/3 of the distance + Time taken for the last 1/3 of the distance

(D / 37.5) = ((2/3) * D / 50) + ((1/3) * D / x)

Simplifying the equation:

1 / 37.5 = 2 / 50 + 1 / x

To find x, we can solve this equation.

Calculation

Let's solve the equation to find the speed of the taxi for the last third of the journey.

1 / 37.5 = 2 / 50 + 1 / x

Multiplying through by 37.5 * 50 * x:

50x = 2 * 37.5 * x + 37.5 * 50

50x - 2 * 37.5 * x = 37.5 * 50

12.5x = 37.5 * 50

x = (37.5 * 50) / 12.5

x = 150

Answer

The speed of the taxi for the last third of the journey is 150 km/h.

Explanation

The speed of the taxi for the last third of the journey is calculated by solving the equation (1 / 37.5) = (2 / 50) + (1 / x). After simplifying the equation, we find that x = 150. Therefore, the speed of the taxi for the last third of the journey is 150 km/h.