Question

Автомашина со скоростью 50 км/ч отправляется из города А в город В. Прибыв в В, она сразу же выезжает обратно. С какой средней скоростью она вернулась из В в А, если известно, что весь путь проехала со средней скоростью 60 км/ч?

Answer 1

1)  60*2=120 (км/ч) - суммарная скорость
2) 120 -50 =70 (км/ч) - скорость на обратном пути
ответ 70 км/ч

Answer 2

Problem Analysis

We are given that a car travels from city A to city B at a speed of 50 km/h and immediately returns from city B to city A. We need to determine the average speed at which the car returned from city B to city A, given that the entire journey was completed at an average speed of 60 km/h.

Solution

To solve this problem, we can use the concept of average speed. The average speed is defined as the total distance traveled divided by the total time taken. Since the distance from city A to city B is the same as the distance from city B to city A, we can assume that the total distance traveled is twice the distance between the two cities.

Let's denote the distance between city A and city B as d. The time taken to travel from city A to city B at a speed of 50 km/h is given by t1 = d / 50. Similarly, the time taken to travel from city B to city A at an unknown speed is given by t2 = d / v, where v is the unknown speed.

We are also given that the entire journey was completed at an average speed of 60 km/h. The total time taken for the journey is given by t = 2d / 60.

Using the equation t = t1 + t2, we can solve for v.

Calculation

Substituting the values of t1, t2, and t into the equation t = t1 + t2, we get:

2d / 60 = d / 50 + d / v

Simplifying the equation, we have:

2 / 60 = 1 / 50 + 1 / v

To solve for v, we can cross-multiply and solve for v:

2v = 60 * (50 + v)

2v = 3000 + 60v

2v - 60v = 3000

-58v = 3000

v = -3000 / 58

v ≈ -51.72

Since speed cannot be negative, we can ignore the negative sign and take the absolute value of v:

v ≈ 51.72 km/h

Answer

The car returned from city B to city A at an average speed of approximately 51.72 km/h.

Explanation

When the car travels from city A to city B at a speed of 50 km/h, it takes a certain amount of time. When it returns from city B to city A at a different speed, it takes a different amount of time. The average speed for the entire journey is calculated by dividing the total distance traveled by the total time taken. By setting up an equation using the average speed and the individual speeds and times, we can solve for the unknown speed. In this case, the car returned from city B to city A at an average speed of approximately 51.72 km/h.

Please note that the negative sign in the calculation is ignored because speed cannot be negative.