Question

Расстояние между селами 36 км один велосипедист преодолевает на 1 ч быстрее другого. Найти скорость каждого велосипедиста, если известно, что скорость одного на 3 км/ч больше скорости другого.

Answer 1

х-скорость одного. тогда (х+3) -скорость другого. Составляем уравнеие:

 

36/х = 36/(х+3) + 1

ОДЗ: х больше 0

домножим все на общий знаменатель: х(х+3):

 

36(х+3) = 36х+х(х+3)

36х+108=36х+х²+3х

х²+3х-108=0

Д=9+432=441-2 корня

х1 = (-3+21)/2 = 9 (км/ч) - скорость одного

х2=(-3-21)/2 = -12 - не удовлетворяет ОДЗ

 

ТОгда скорость другого равна: 9+3 = 12 (км/ч)

 

Ответ: 9км/ч и 12км/ч.

Answer 2

Problem Analysis

We are given that the distance between two villages is 36 km. One cyclist covers this distance 1 hour faster than the other cyclist. We need to find the speed of each cyclist, given that the speed of one cyclist is 3 km/h faster than the speed of the other cyclist.

Solution

Let's assume the speed of the slower cyclist is x km/h. Then the speed of the faster cyclist would be x + 3 km/h.

We can use the formula speed = distance / time to calculate the time taken by each cyclist to cover the distance of 36 km.

For the slower cyclist: time = distance / speed = 36 / x

For the faster cyclist: time = distance / speed = 36 / (x + 3)

We are given that the slower cyclist takes 1 hour more than the faster cyclist to cover the distance. So we can set up the equation:

36 / x = 36 / (x + 3) + 1

Let's solve this equation to find the value of x.

Calculation

To solve the equation, we can start by multiplying both sides by x(x + 3) to eliminate the denominators:

36(x + 3) = 36x + x(x + 3)

Expanding and simplifying:

36x + 108 = 36x + x^2 + 3x

Combining like terms:

x^2 + 3x - 108 = 0

Now we have a quadratic equation. We can solve it by factoring or using the quadratic formula. Let's use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, a = 1, b = 3, and c = -108. Substituting these values into the formula:

x = (-3 ± √(3^2 - 4(1)(-108))) / (2(1))

Simplifying further:

x = (-3 ± √(9 + 432)) / 2

x = (-3 ± √441) / 2

x = (-3 ± 21) / 2

We have two possible solutions for x:

1. x = (-3 + 21) / 2 = 18 2. x = (-3 - 21) / 2 = -12

Since speed cannot be negative, we discard the second solution.

Therefore, the speed of the slower cyclist is 18 km/h and the speed of the faster cyclist is 18 + 3 = 21 km/h.

Answer

The speed of the slower cyclist is 18 km/h and the speed of the faster cyclist is 21 km/h.