Question

Из пунк­та A в пункт B од­но­вре­мен­но вы­еха­ли два ав­то­мо­би­ля. Пер­вый про­ехал с по­сто­ян­ной ско­ро­стью весь путь. Вто­рой про­ехал первую по­ло­ви­ну пути со ско­ро­стью 24 км/ч, а вто­рую по­ло­ви­ну пути – со ско­ро­стью, на 16 км/ч боль­шей ско­ро­сти пер­во­го, в ре­зуль­та­те чего при­был в пункт B од­но­вре­мен­но с пер­вым ав­то­мо­би­лем. Най­ди­те ско­рость пер­во­го ав­то­мо­би­ля. Ответ дайте в км/ч.

Answer 1

В О Т.Теперь точно правильно.

Answer 2

Problem Analysis

We are given that two cars simultaneously traveled from point A to point B. The first car traveled the entire distance at a constant speed. The second car traveled the first half of the distance at a speed of 24 km/h and the second half at a speed 16 km/h faster than the first car. The second car arrived at point B at the same time as the first car. We need to find the speed of the first car in km/h.

Solution

Let's assume the distance from point A to point B is d km.

The first car traveled the entire distance at a constant speed, so the time taken by the first car is given by:

Time taken by first car = Distance / Speed of first car

The second car traveled the first half of the distance at a speed of 24 km/h and the second half at a speed 16 km/h faster than the first car. So, the time taken by the second car is given by:

Time taken by second car = (Distance / 2) / 24 + (Distance / 2) / (Speed of first car + 16)

Since both cars arrived at point B at the same time, the time taken by both cars is equal. Therefore, we can set up the following equation:

(Distance / Speed of first car) = (Distance / 2) / 24 + (Distance / 2) / (Speed of first car + 16)

Now, let's solve this equation to find the speed of the first car.

Calculation

Let's solve the equation step by step:

(Distance / Speed of first car) = (Distance / 2) / 24 + (Distance / 2) / (Speed of first car + 16)

Multiplying both sides of the equation by the Speed of first car:

Distance = (Distance / 2) * (Speed of first car) / 24 + (Distance / 2)

Multiplying both sides of the equation by 24:

24 * Distance = (Distance / 2) * (Speed of first car) + 12 * Distance

Simplifying the equation:

24 * Distance = (Distance * (Speed of first car)) / 2 + 12 * Distance

Multiplying both sides of the equation by 2:

48 * Distance = Distance * (Speed of first car) + 24 * Distance

Combining like terms:

48 * Distance = (Speed of first car) * Distance + 24 * Distance

Subtracting Distance from both sides of the equation:

47 * Distance = (Speed of first car) * Distance

Dividing both sides of the equation by Distance:

47 = Speed of first car

Therefore, the speed of the first car is 47 km/h.

Answer

The speed of the first car is 47 km/h.