Question

З міста А до міста В, відстань між якими 420 км, вирушив автомобіль. Через 2 год після цього з міста В до міста А вирушив мотоцикліст, який зустрівся з автомобілем через 1 год після свого виїзду. Мотоцикліст долає відстань між містами А та В на 1 год 52 хв швидше, ніж автомобіль. Знайдіть швидкості руху автомобіля та мотоцикліста

Answer 1

Ответ:

х км/ч - скорость автобуса

х + 20 км/ч - скорость автомобиля

20 минут = 1/3 часа

\begin{gathered} \frac{1}{3}x+(x + x + 20) *2=300 \\ \\ \frac{1}{3}x+4x+40=300 \\ \\ x+2x+120=900 \\ \\ 13x=780\end{gathered}31x+(x+x+20)∗2=30031x+4x+40=300x+2x+120=90013x=780

Answer 2

Problem Analysis

We are given that the distance between city A and city B is 420 km. An automobile starts from city A and after 2 hours, a motorcyclist starts from city B. The motorcyclist meets the automobile 1 hour after starting. The motorcyclist covers the distance between the two cities 1 hour and 52 minutes faster than the automobile. We need to find the speeds of the automobile and the motorcyclist.

Solution

Let's assume the speed of the automobile is x km/h and the speed of the motorcyclist is y km/h.

We know that the distance between city A and city B is 420 km. The time taken by the automobile to cover this distance is 2 hours less than the time taken by the motorcyclist. Therefore, the time taken by the automobile is t hours and the time taken by the motorcyclist is t + 2 hours.

We can use the formula speed = distance / time to calculate the speeds of the automobile and the motorcyclist.

The speed of the automobile is given by: x = 420 / t [[1]]

The speed of the motorcyclist is given by: y = 420 / (t + 2) [[2]]

We are also given that the motorcyclist covers the distance between the two cities 1 hour and 52 minutes faster than the automobile. This can be expressed as: t + 2 = t + 1 + 52/60 [[3]]

Now, we can solve equations [[1]], [[2]], and [[3]] to find the values of x and y.

Calculation

Let's solve the equations:

From equation [[3]]: t + 2 = t + 1 + 52/60

Simplifying the equation: 2 = 1 + 52/60 2 = 1 + 13/15 2 = 15/15 + 13/15 2 = 28/15

Multiplying both sides of the equation by 15 to get rid of the fraction: 2 * 15 = 28/15 * 15 30 = 28

This is not a valid equation, which means there is no solution to the problem. There might be an error in the given information or the problem itself.

Conclusion

Based on the given information, there is no valid solution to find the speeds of the automobile and the motorcyclist. It is recommended to double-check the problem statement or provide additional information to solve the problem accurately.