Question

Помогите \ Машина груженая капустой,выехала из деревни в город. Она ехала со скоростью 45км/ч и пробыла в пути 6 ч. Обратный путь она преодолела за 3 ч. С какой скоростью машина ехала обратно в деревню? Реши двумя способами

Answer 1

1) 45 Х 6 = 270 км растояние между деревней и городом

    270/3=90 км/ч  скорость машины на обратном пути

2) Пусть х  км /ч скорость на обратном пути, то

    45 Х 6= х Х 3

  х = (45 Х 6)/3

  х =90 км/ч

Answer 2

Problem Analysis

We are given that a car loaded with cabbage traveled from a village to a city at a speed of 45 km/h and took 6 hours to complete the journey. The return journey from the city to the village took 3 hours. We need to determine the speed at which the car traveled on the return journey.

Solution 1: Using Distance-Speed-Time Formula

We can use the formula Distance = Speed × Time to solve this problem. Let's denote the distance from the village to the city as D1 and the distance from the city to the village as D2.

For the first journey: - Speed = 45 km/h - Time = 6 hours - Distance = D1

Using the formula, we have: D1 = Speed × Time D1 = 45 km/h × 6 hours D1 = 270 km

For the return journey: - Time = 3 hours - Distance = D2

Using the formula, we have: D2 = Speed × Time D2 = Speed × 3 hours

Since the distance traveled on the return journey is the same as the distance traveled on the first journey (D1 = D2), we can equate the two equations: D1 = D2 45 km/h × 6 hours = Speed × 3 hours

Simplifying the equation, we can solve for the speed: 45 km/h × 6 hours = Speed × 3 hours 270 km = Speed × 3 hours

Dividing both sides of the equation by 3 hours, we get: Speed = 270 km / 3 hours Speed = 90 km/h

Therefore, the car traveled back to the village at a speed of 90 km/h.

Solution 2: Using the Ratio of Times

Another way to solve this problem is by using the ratio of times. Since the distance traveled on the first journey is the same as the distance traveled on the return journey, the ratio of the times taken for the two journeys will be the inverse of the ratio of their speeds.

Let's denote the speed of the return journey as S2.

For the first journey: - Speed = 45 km/h - Time = 6 hours

For the return journey: - Speed = S2 (unknown) - Time = 3 hours

The ratio of times is: Time1 / Time2 = 6 hours / 3 hours Time1 / Time2 = 2

The ratio of speeds is the inverse of the ratio of times: Speed2 / Speed1 = 1 / (Time1 / Time2) Speed2 / 45 km/h = 1 / 2

Simplifying the equation, we can solve for the speed of the return journey: Speed2 = 45 km/h / 2 Speed2 = 22.5 km/h

Therefore, the car traveled back to the village at a speed of 22.5 km/h.

Conclusion

The car traveled back to the village at a speed of 90 km/h (Solution 1) or 22.5 km/h (Solution 2), depending on the method used to solve the problem.