Question

Длина обода (окружности) переднего колеса кареты равна 1,5 м, а заднего 4 м. Какое расстояние проехала карета, если ее переднее колесо сделало на 250 оборотов больше, чем заднее?

Answer 1

Пусть пройденный путь в метрах равен х, тогда
x / 1.5 - 250 = x / 4
Домножаем на 12 обе части.

8 * x - 3000 = 3 * x
5 * x = 3000
x = 600

Т.е. 600 метров

Answer 2

Calculation of the Distance Traveled by the Carriage

To calculate the distance traveled by the carriage, we need to determine the circumference of the front and rear wheels and then find the difference in the number of rotations between them.

Given: - The circumference of the front wheel is 1.5 m. - The circumference of the rear wheel is 4 m. - The front wheel made 250 more rotations than the rear wheel.

Calculating the Circumference of the Wheels

The circumference of a circle can be calculated using the formula: C = 2πr, where C is the circumference and r is the radius of the circle.

Let's calculate the radius of the front and rear wheels using the given circumferences:

- For the front wheel: - Circumference = 1.5 m - Radius = Circumference / (2π) = 1.5 / (2π) = 0.2387 m (rounded to four decimal places)

- For the rear wheel: - Circumference = 4 m - Radius = Circumference / (2π) = 4 / (2π) = 0.6366 m (rounded to four decimal places)

Calculating the Difference in Rotations

The difference in the number of rotations between the front and rear wheels is given as 250 rotations.

Calculating the Distance Traveled

To calculate the distance traveled by the carriage, we need to find the difference in the distances covered by the front and rear wheels.

The distance covered by a wheel in one rotation is equal to its circumference.

Let's calculate the distance covered by the front and rear wheels:

- For the front wheel: - Distance covered = Circumference = 1.5 m

- For the rear wheel: - Distance covered = Circumference = 4 m

The difference in the distances covered by the front and rear wheels is given by:

Difference in distance = (Distance covered by front wheel - Distance covered by rear wheel) * Difference in rotations

Substituting the values:

Difference in distance = (1.5 - 4) * 250 = -2.5 * 250 = -625 m

The negative sign indicates that the carriage moved in the opposite direction of the front wheel.

Therefore, the carriage traveled a distance of 625 meters in the opposite direction of the front wheel.