Question

Из двух сел расстояние между которыми 26 км выехали одновременно навстречу друг друг у два велосипедиста и встретились через 1 ч после начала движения .Найдите скорость каждого из них , если первый за 3 ч проезжает на 8 км больше, чем второй за 2 ч

Answer 1

Х - скорость первого, у - скорость второго
система х+у=26
             3х-8=2у
система 2х+2у=52
             3х-2у=8
2х+3х=52+8
5х=60
х=60/5=12
у=26-12=14
ответ 12км/ч и 14км/ч

Answer 2

Problem Analysis

We have two cyclists who start from two different villages and meet each other after 1 hour. The distance between the villages is 26 km. The first cyclist travels 8 km more than the second cyclist in 3 hours, while the second cyclist travels for 2 hours. 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.

We know that the distance traveled by the first cyclist in 3 hours is 8 km more than the distance traveled by the second cyclist in 2 hours. So we can write the following equation:

3x = 2y + 8 We also know that the total distance between the villages is 26 km, and the time taken to meet each other is 1 hour. So we can write the following equation:

x + y = 26 We have a system of two equations with two variables. We can solve this system of equations to find the values of x and y.

Solving the System of Equations

We can solve the system of equations by substitution or elimination. Let's use the elimination method.

From equation we can rewrite it as:

x = 26 - y Substituting equation into equation we get:

3(26 - y) = 2y + 8

Simplifying the equation:

78 - 3y = 2y + 8

Moving all the terms to one side:

5y = 70

Dividing both sides by 5:

y = 14

Substituting the value of y back into equation we get:

x = 26 - 14 = 12

Answer

The speed of the first cyclist is 12 km/h and the speed of the second cyclist is 14 km/h.

Verification

Let's verify our answer by substituting the values of x and y into the original equations.

From equation 3x = 2y + 8 3(12) = 2(14) + 8 36 = 28 + 8 36 = 36

From equation x + y = 26 12 + 14 = 26 26 = 26

The values satisfy both equations, so our answer is correct.

Conclusion

The first cyclist has a speed of 12 km/h, and the second cyclist has a speed of 14 km/h.