Question

Решить задачу. Две машины ехали с одинаковой скоростью. Первая машина была в дороге 8ч, а вторая-3ч. Первая машина проехала на 320км больше, чем вторая. Какое расстояние проехала каждая машина?

Answer 1

1) 8 - 3 = 5 (часов), за которые 1-ая машина проехала 320км
2) 320 : 5 = 64(км/ч) - скорость каждой машины
3) 64 * 8 = 512(км) проехала 1-ая машина
4) 64 * 3 =192(км) проехала 2-а машина.
Ответ: 512км - первая машина; 192км - вторая машина.

Answer 2

Problem Analysis

We are given two cars traveling at the same speed. The first car takes 8 hours to travel a certain distance, while the second car takes 3 hours to travel the same distance. The first car travels 320 km more than the second car. We need to find the distance traveled by each car.

Solution

Let's assume the distance traveled by the second car is x km. Since the first car travels 320 km more, the distance traveled by the first car is x + 320 km.

We can use the formula distance = speed × time to solve this problem. Since both cars are traveling at the same speed, we can set up the following equations:

For the first car: distance = speed × time x + 320 = speed × 8 For the second car: distance = speed × time x = speed × 3 To solve this system of equations, we can divide equation by equation:

(x + 320) / x = (speed × 8) / (speed × 3)

Simplifying the equation, we get:

(x + 320) / x = 8 / 3

Cross-multiplying, we have:

3(x + 320) = 8x

Expanding and simplifying, we get:

3x + 960 = 8x

Subtracting 3x from both sides, we have:

960 = 5x

Dividing both sides by 5, we get:

x = 192

Therefore, the second car traveled 192 km, and the first car traveled 192 + 320 = 512 km.

Answer

The second car traveled 192 km, and the first car traveled 512 km.

Verification

Let's verify our answer using the given information. The first car took 8 hours to travel 512 km, which means its speed was 512 km / 8 hours = 64 km/h. The second car took 3 hours to travel 192 km, which means its speed was 192 km / 3 hours = 64 km/h. Since both cars traveled at the same speed, our answer is correct.

Conclusion

The second car traveled 192 km, and the first car traveled 512 km.