Question

Когда мальчик прошел по мосту расстояние, составляющее α = 0,35 от полной длины моста, он услышал сзади себя сигнал догоняющего его автомобиля, в котором ехал его отец. Желая поскорее увидеться с отцом, мальчик развернулся и побежал навстречу автомобилю, поравнявшись с ним у начала моста. Известно, что если бы мальчик побежал бы с той же скоростью не назад, а вперед, то автомобиль нагнал бы его у конца моста. Во сколько раз n скорость автомобиля больше скорости мальчика? Ответ округлите до двух знаков после запятой

Answer 1

Пусть расстояние от авто до моста равно х, скорость ребенка = Vр, скорость авто = Vm. Тогда $\frac{x + l}{Vm} = \frac{0,65l}{Vp}$ и $\frac{0,35l}{Vp} = \frac{x}{Vm}$. Значит х = 1,16666 l. Подставляем во вторую формулу и получаем $\frac{Vm}{Vp} = \frac{x}{0,35l}$ и равняется 3,3333, ≈ 3,33

Answer 2

Problem Analysis

A boy is running on a bridge and hears a signal from a car approaching him from behind. If the boy had run forward with the same speed, the car would have caught up with him at the end of the bridge. We need to find the ratio of the car's speed to the boy's speed.

Solution

Let's assume the total length of the bridge is L. The boy hears the signal when he has covered a distance of αL (where α = 0.35) from the starting point of the bridge. If the boy had run forward with the same speed, he would have covered a distance of (1-α)L and the car would have caught up with him at the end of the bridge.

Let's assume the speed of the boy is v and the speed of the car is n*v (where n is the ratio we need to find).

To solve this problem, we can use the concept of relative speed. The relative speed of the car with respect to the boy is the difference between their speeds: (n-1)v. The time taken by the car to cover the distance αL is the same as the time taken by the boy to cover the distance (1-α)L.

Using the formula time = distance / speed, we can write the following equation:

(αL) / (n-1)v = [(1-α)L] / v

Simplifying the equation, we get:

α / (n-1) = (1-α)

Solving for n, we get:

n = 1 + (1/α)

Now we can substitute the value of α (0.35) into the equation to find the value of n.

Calculation

Let's calculate the value of n:

n = 1 + (1/0.35) = 1 + 2.857 = 3.857

Therefore, the speed of the car is approximately 3.857 times the speed of the boy.

Answer

The speed of the car is approximately 3.857 times the speed of the boy.