Question

С одного города в другой, расстояние между которыми 300 км, выехали одновременно две машины. Одна со скоростью на 10 км/я больше, чем вторая , поэтому прибыла к пункту назначения на 1 час раньше второй. Найти скорость каждого автомобиля

Answer 1

Пусть х - скорость 1 машины, тогда х+10 - скорость 2 машины. 300/х - время 1, 300/(х+10) + время 2 (300/х)-(300/(х+10))=1 3000/х^2+10х=1 х^2+10х-3000=0 х1=(10-110)/2 х2=(10+110)/2 х1=-50 неверно х2=60=> Ответ 60 и 70

Answer 2

Problem Analysis

We have two cars traveling from one city to another, a distance of 300 km. One car is traveling 10 km/h faster than the other. The first car arrives at the destination 1 hour earlier than the second car. We need to find the speed of each car.

Solution

Let's assume the speed of the slower car is x km/h. Therefore, the speed of the faster car is x + 10 km/h.

We can use the formula distance = speed × time to calculate the time taken by each car to travel the distance of 300 km.

For the slower car: 300 = x × t1 (Equation 1)

For the faster car: 300 = (x + 10) × t2 (Equation 2)

We also know that the first car arrived 1 hour earlier than the second car, so the time taken by the second car is 1 hour more than the time taken by the first car: t2 = t1 + 1 (Equation 3)

We can solve this system of equations to find the values of x, t1, and t2.

Calculation

Let's solve the system of equations:

From Equation 1, we can express t1 in terms of x: t1 = 300 / x

Substituting this value of t1 in Equation 3, we get: t2 = (300 / x) + 1

Substituting the values of t1 and t2 in Equation 2, we get: 300 = (x + 10) × ((300 / x) + 1)

Simplifying this equation, we get: 300 = (x + 10) × (300 + x) / x

Cross-multiplying, we get: 300x = (x + 10) × (300 + x)

Expanding the equation, we get: 300x = 300x + 10x + 3000 + x^2

Simplifying further, we get: 0 = x^2 + 10x + 3000

This is a quadratic equation. We can solve it by factoring or using the quadratic formula. Let's use the quadratic formula to find the values of x.

The quadratic formula is given by: x = (-b ± √(b^2 - 4ac)) / (2a)

In our equation, a = 1, b = 10, and c = 3000.

Substituting these values in the quadratic formula, we get: x = (-10 ± √(10^2 - 4 × 1 × 3000)) / (2 × 1)

Simplifying further, we get: x = (-10 ± √(100 - 12000)) / 2

x = (-10 ± √(-11900)) / 2

Since the value inside the square root is negative, the quadratic equation has no real solutions. This means that there is no possible combination of speeds for the two cars that satisfies the given conditions.

Therefore, there is no solution to this problem.

Conclusion

Based on the given information, there is no possible combination of speeds for the two cars that would allow the first car to arrive at the destination 1 hour earlier than the second car.