Question

1) Диаметр переднего колеса велосипеда в полтора раза больше диаметра заднего колеса. Во время движения велосипеда его переднее колесо совершает 5 оборотов за одну секунду. Сколько оборотов совершает при этом за секунду заднее колесо? 2) За какое время совершают один оборот переднее и заднее колеса при той же скорости движения?

Answer 1

1) Диаметр переднего колеса велосипеда в полтора раза больше диаметра заднего колеса. Во время движения велосипеда его переднее колесо совершает 5 оборотов за одну секунду. Сколько оборотов совершает при этом за секунду заднее колесо?

To find out how many revolutions the rear wheel makes in one second, we need to determine the ratio of the diameters of the front and rear wheels. Given that the diameter of the front wheel is one and a half times larger than the diameter of the rear wheel, we can calculate the number of revolutions of the rear wheel.

Let's assume that the rear wheel makes x revolutions in one second. Since the diameter of the front wheel is one and a half times larger than the diameter of the rear wheel, the circumference of the front wheel is also one and a half times larger than the circumference of the rear wheel.

The formula to calculate the number of revolutions is:

Number of revolutions = Distance traveled / Circumference

Since the distance traveled by both wheels is the same, we can set up the following equation:

5 revolutions (front wheel) = x revolutions (rear wheel)

Since the circumference of the front wheel is one and a half times larger than the circumference of the rear wheel, we can write:

5 * (1.5 * Circumference of rear wheel) = x * Circumference of rear wheel

Simplifying the equation, we get:

7.5 * Circumference of rear wheel = x * Circumference of rear wheel

The circumference of the rear wheel cancels out, and we are left with:

7.5 = x

Therefore, the rear wheel makes 7.5 revolutions in one second.