Question

Из города а в город в одновременно выехали два автомобилиста первый проехал с постоянной скоростью весь путь.Второй проехал первую половину пути со скоростью 33 км/ч, а вторую половину пути-со скоростью,на 22 км/ч большей скорости первого, в результате чего прибыл в В одновременно с первым автомобилистом. Найдите скорость первого автомобилиста.Дайте ответ в км/ч

Answer 1

Составим уравнения. 
$\frac{2}{(v_{1})}=\frac{1}{33}+\frac{2}{(v_{1}+22)}$  -- приехали одновременно (сократили на длину пути, по сути записали t = t_1 + t_2)

Теперь решаем уравнение. Приведем к общему знаменателю 
$33v_{1}(v_{1}+22)$ и сократим

$66(v_{1}+22) = v_{1}(v_{1}+22) + 33v_1$

$v^2-11v-1452=0$

Решая уравнение, получаем 2 корня: -33 и 44. Отрицательный нам не подходит, ибо скорость величина положительная. Ответ: 44 км/ч

Answer 2

Problem Analysis

We have two drivers who simultaneously left one city and arrived at another city. The first driver traveled the entire distance at a constant speed. The second driver traveled the first half of the distance at a speed of 33 km/h and the second half at a speed 22 km/h faster than the first driver's speed. We need to find the speed of the first driver.

Solution

Let's assume the distance between the two cities is D km.

The first driver traveled the entire distance at a constant speed, which we'll call x km/h.

The second driver traveled the first half of the distance at a speed of 33 km/h and the second half at a speed 22 km/h faster than the first driver's speed. Therefore, the second driver's speeds were 33 km/h and x + 22 km/h for the first and second halves of the distance, respectively.

To find the speed of the first driver, we can set up an equation based on the time it took for both drivers to reach the destination.

The time taken by the first driver is given by:

Time taken by first driver = Distance / Speed = D / x

The time taken by the second driver is the sum of the times taken for the first and second halves of the distance:

Time taken by second driver = (0.5D) / 33 + (0.5D) / (x + 22)

Since both drivers arrived at the destination simultaneously, their times must be equal:

D / x = (0.5D) / 33 + (0.5D) / (x + 22)

To solve this equation for x, we can multiply both sides by x(x + 22) to eliminate the denominators:

D(x + 22) = (0.5D)(x + 22) + (0.5D)x

Simplifying the equation:

Dx + 22D = 0.5Dx + 11D + 0.5Dx

Combining like terms:

Dx + 22D = Dx + 11D + Dx

Simplifying further:

Dx + 22D = 2Dx + 11D

Rearranging the equation:

Dx - 2Dx = 11D - 22D

Simplifying:

-Dx = -11D

Dividing both sides by -D:

x = 11

Therefore, the speed of the first driver is 11 km/h.

Answer

The speed of the first driver is 11 km/h.