Question

два велосипедиста выезжают одновременно навстречу друг другу из пунктов А и В , расстояние между которыми равно 54 км, и через 2 часа встречаются. не останавливаясь, они продолжают путь с той же скоростью, и второй прибывает в пункт А на 54 минуты раньше , чем первый в пункт В. найдите скорость каждого велосипедиста.

Answer 1

Problem Analysis

We have two cyclists starting simultaneously from points A and B, which are 54 km apart. After 2 hours, they meet each other. They continue their journey without stopping, and the second cyclist arrives at point A 54 minutes earlier than the first cyclist arrives at point B. We need to find the speed of each cyclist.

Solution

Let's assume the speed of the first cyclist is x km/h and the speed of the second cyclist is y km/h.

To find the speed of each cyclist, we can use the formula:

Speed = Distance / Time

We know that the distance between points A and B is 54 km. After 2 hours, the first cyclist has traveled for 2 hours at speed x, and the second cyclist has traveled for 2 hours at speed y. Therefore, the distance traveled by each cyclist after 2 hours is:

First cyclist: 2x km

Second cyclist: 2y km

After they meet, they continue their journey for a certain amount of time until the first cyclist reaches point B and the second cyclist reaches point A. The time taken by the first cyclist to reach point B is the same as the time taken by the second cyclist to reach point A, minus 54 minutes.

Let's calculate the time taken by the second cyclist to reach point A. Since the distance between points A and B is 54 km, the time taken by the second cyclist to cover this distance at speed y is:

Time taken by second cyclist = Distance / Speed = 54 / y hours

The time taken by the first cyclist to reach point B is the same as the time taken by the second cyclist to reach point A, minus 54 minutes. We need to convert 54 minutes to hours by dividing it by 60:

Time taken by first cyclist = Time taken by second cyclist - (54 / 60) hours

Now, we can set up the equation:

2x = 54 - (54 / 60) + 2y

Simplifying the equation:

2x = 54 - 0.9 + 2y

2x = 53.1 + 2y

Now, we have two equations:

2x = 53.1 + 2y (Equation 1)

2x = 2y (Equation 2)

We can solve this system of equations to find the values of x and y.

Solving the System of Equations

Subtracting Equation 2 from Equation 1, we get:

53.1 + 2y - 2y = 2x - 2x

Simplifying the equation:

53.1 = 0

This equation is not possible, which means there is no solution to the system of equations. It seems there might be an error in the problem statement or the given information.

Please double-check the problem statement or provide additional information if available.