Question

Два лыжника вышли одновременно навстречу друг другу.Скорость одного лыжника на 3км/ч больше другого.К моменту встречи один лыжник прошёл 32 км .а другой 44 км.Сколько времени были в пути лыжники.Найдите скорость каждого лыжника.

Answer 1

32/х=44/(х+3)

44х=32х+96

12х=96

х=8км/ч - скоростьпервого

8+3=11км/ч - скорость второго

32/8=4часа - время в пути

Answer 2

приведем скорость второго лыжника к единой единице измерения

200 м/мин = 12000 м/ч =12 км/ч

первый лыжник бежит быстрее

15-12=3 км/ч

Ответ: первый лыжник бежит быстрее на 3 км/ч

Answer 3

Problem Statement

Два лыжника вышли одновременно навстречу друг другу. Скорость одного лыжника на 3 км/ч больше другого. К моменту встречи один лыжник прошёл 32 км, а другой 44 км. Сколько времени были в пути лыжники? Найдите скорость каждого лыжника.

Solution

To find the time taken by the skiers and their respective speeds, we can use the formula:

Time = Distance / Speed

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

We know that the slower skier traveled a distance of 32 km and the faster skier traveled a distance of 44 km.

Using the formula, we can calculate the time taken by each skier:

Time taken by the slower skier = Distance / Speed = 32 / x

Time taken by the faster skier = Distance / Speed = 44 / (x + 3)

To find the total time taken by both skiers, we can add their individual times:

Total time = Time taken by the slower skier + Time taken by the faster skier

Let's calculate the values:

Time taken by the slower skier = 32 / x

Time taken by the faster skier = 44 / (x + 3)

Total time = (32 / x) + (44 / (x + 3))

Now, we can solve this equation to find the value of x and then calculate the speeds of both skiers.

Let's solve the equation:

32 / x + 44 / (x + 3) = Total time

To simplify the equation, we can multiply both sides by x(x + 3) to eliminate the denominators:

32(x + 3) + 44x = Total time * x(x + 3)

Simplifying further:

32x + 96 + 44x = Total time * (x^2 + 3x)

76x + 96 = Total time * x^2 + Total time * 3x

Rearranging the equation:

Total time * x^2 + (Total time * 3 - 76) * x + 96 = 0

Now, we can solve this quadratic equation to find the value of x, which represents the speed of the slower skier.

Once we have the value of x, we can calculate the speed of the faster skier by adding 3 km/h to x.

Let's solve the equation and find the values: