Question

От села до города легковая машина доехала за 3 часа, а грузовая за 6 часов. Найдите скорость легковой машины, если скорость грузовика на 24 км/ч меньше скорости легковой. Решить уровнением многочленов

Answer 1

Ответ:

48 км/ч

Объяснение:

Возьмём за x - скорость легковой машины, значит скорость грузовика равна x-24.

Из этого следует, что 6(x-24) = 3x

6x-144 = 3x

6x-3x = 144

3x = 144

x = 48 км/ч

Answer 2

I can help you with your math problem. Here is a detailed solution:

Let $x$ be the speed of the car and $y$ be the speed of the truck. Then we have the following system of equations:

$$ \begin{cases} x \cdot 3 = y \cdot 6 \\ x = y + 24 \end{cases} $$

To solve this system, we can substitute the second equation into the first one and get:

$$ (y + 24) \cdot 3 = y \cdot 6 $$

Simplifying and rearranging, we get:

$$ y^2 - 36y - 144 = 0 $$

This is a quadratic equation that can be solved by using the quadratic formula:

$$ y = \frac{-(-36) \pm \sqrt{(-36)^2 - 4 \cdot 1 \cdot (-144)}}{2 \cdot 1} $$

Simplifying, we get:

$$ y = \frac{36 \pm 24}{2} $$

There are two possible values for $y$:

$$ y = 30 \text{ or } y = 6 $$

However, only one of them makes sense in the context of the problem. If $y = 6$, then $x = y + 24 = 30$, which means that the car and the truck have the same speed. This contradicts the fact that the car reached the city faster than the truck. Therefore, we reject this solution and conclude that $y = 30$.

Then, we can find $x$ by using the second equation:

$$ x = y + 24 = 30 + 24 = 54 $$

Therefore, the speed of the car is 54 km/h and the speed of the truck is 30 km/h.

I hope this helps. If you want to check your answer or practice more problems, you can visit [this website](https://uchi.ru/otvety/questions/ot-sela-do-goroda-legkovaya-mashina-doehala-za-2-chasa-a-gruzovaya-za-5-chasov-naydite-sk).