Question

Мальчик прошел 240 м,если бы его шаг был на 20 см длинее,то он бы прошел на 100 шагов меньше.Найти длину шага. С объяснением !!!

Answer 1

Х-длина шага,24000/х-число шагов
х+20-если бы был шаг,24000/(х+20) число шагов
24000/х-24000/(х+20)=100
100х(х+20)-24000(х+20-х)=0
100х²+2000х-480000=0
х²+20х-4800=0
х1+х2=-20 и х1*х2=-4800
х1=-80 и х2=60см длина шага

Answer 2

Problem Analysis

We are given that a boy walked a distance of 240 meters. If his step was 20 cm longer, he would have taken 100 fewer steps. We need to find the length of his step.

Solution

Let's assume the length of the boy's original step is x cm. According to the problem, if his step was 20 cm longer, the new step length would be x + 20 cm.

We can set up the following equation based on the given information:

240 / x = (240 / (x + 20)) + 100

To solve this equation, we can follow these steps:

1. Multiply both sides of the equation by x(x + 20) to eliminate the denominators. 2. Simplify the equation. 3. Solve for x.

Let's solve the equation step by step:

1. Multiply both sides of the equation by x(x + 20):

240(x + 20) = 240x + 100x(x + 20)

2. Simplify the equation:

240x + 4800 = 240x + 100x^2 + 2000x

Simplifying further:

100x^2 + 2000x - 4800 = 0

3. Solve for x using the quadratic formula:

The quadratic formula is given by:

x = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, a = 100, b = 2000, and c = -4800.

Plugging in these values into the quadratic formula:

x = (-2000 ± √(2000^2 - 4 * 100 * -4800)) / (2 * 100)

Simplifying further:

x = (-2000 ± √(4000000 + 1920000)) / 200

x = (-2000 ± √(5920000)) / 200

x = (-2000 ± 2429.68) / 200

We have two possible solutions:

x = (-2000 + 2429.68) / 200 or x = (-2000 - 2429.68) / 200

Calculating these values:

x = 4.1484 or x = -24.1484

Since the length of a step cannot be negative, we discard the negative solution.

Therefore, the length of the boy's step is approximately 4.1484 cm.

Answer

The length of the boy's step is approximately 4.1484 cm.