Question

Пони и ослик бегали с постоянными скоростями по кругу длиной 100 м. Пони каждые две минуты обгонял ослика. Когда ослик вдвое увеличил скорость, он сам стал каждые две минуты обгонять пони. С какими скоростями бегали ослик и пони первоначально?

Answer 1

100÷2=50(км)
ответ:ослик и пони бегали со скоростью 50 км в час первоначально

Answer 2

Problem Analysis

We are given that a pony and a donkey are running in a circle with a length of 100 meters. Initially, the pony overtakes the donkey every two minutes. Then, when the donkey doubles its speed, it starts overtaking the pony every two minutes. We need to determine the initial speeds of the pony and the donkey.

Solution

Let's assume the initial speed of the pony is P meters per minute and the initial speed of the donkey is D meters per minute.

When the pony overtakes the donkey every two minutes, it means that in two minutes, the pony completes one full lap more than the donkey. Since the length of the circle is 100 meters, the pony covers 100 meters more than the donkey in two minutes. Therefore, we can set up the following equation:

2P = 2D + 100 Similarly, when the donkey doubles its speed, it starts overtaking the pony every two minutes. This means that in two minutes, the donkey completes one full lap more than the pony. Using the same logic as before, we can set up the following equation:

2D = 2P + 100 Now, we can solve this system of equations to find the initial speeds of the pony and the donkey.

Solving the Equations

Let's solve the system of equations and:

2P = 2D + 100 2D = 2P + 100 We can rearrange equation to solve for P:

2P - 2D = 100

P - D = 50 We can rearrange equation to solve for D:

2D - 2P = 100

D - P = 50 Now, we can solve equations and simultaneously to find the values of P and D.

Adding equations and we get:

(P - D) + (D - P) = 50 + 50

0 = 100

This equation is not possible to solve because it leads to a contradiction. Therefore, there is no solution to the system of equations, and we cannot determine the initial speeds of the pony and the donkey based on the given information.

Conclusion

Based on the given information, we cannot determine the initial speeds of the pony and the donkey. The system of equations does not have a valid solution.