Question

Из A в B одновременно выехали два автомобилиста. Первый проехал с постоянной скоростью весь путь. второй проехал первую половину пути со скоростью 30 км/ч а вторую половину пути проехал со скоростью 9 км/ч больше скорости первого, в результате чего прибыл в B одновременно с первым автомобилистом. Найдите скорость первого автомобилиста. С решением

Answer 1

Это это легко так как они пришли одновременно то один деленное на х равен ноль целых пять деревянные на киевской + написала 5 зеленый на икс + 9

Answer 2

Problem Analysis

We are given that two drivers, A and B, simultaneously traveled from point A to point B. 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 30 km/h and the second half at a speed 9 km/h faster than the first driver. We need to find the speed of the first driver.

Solution

Let's assume the distance between points A and B is d km.

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

The second driver traveled the first half of the distance at a speed of 30 km/h and the second half at a speed 9 km/h faster than the first driver. So, the time taken by the second driver is given by: time taken by second driver = (distance / 2) / 30 + (distance / 2) / (speed of first driver + 9)

Since both drivers arrived at point B simultaneously, the time taken by both drivers is the same. Therefore, we can equate the two expressions for time and solve for the speed of the first driver.

Let's solve the equation:

distance / speed = (distance / 2) / 30 + (distance / 2) / (speed of first driver + 9)

Simplifying the equation:

1 / speed = 1 / 30 + 1 / (speed of first driver + 9)

To solve for the speed of the first driver, we can multiply both sides of the equation by the product of the two denominators:

30(speed of first driver + 9) = speed of first driver(30 + speed of first driver + 9)

Expanding and simplifying the equation:

30speed of first driver + 270 = speed of first driver^2 + 39speed of first driver + 9(speed of first driver) + 9^2

speed of first driver^2 + 9speed of first driver - 30speed of first driver - 39speed of first driver + 270 - 9^2 = 0

speed of first driver^2 - 60speed of first driver + 270 - 81 = 0

speed of first driver^2 - 60speed of first driver + 189 = 0

Now, we can solve this quadratic equation to find the speed of the first driver.

Using the quadratic formula:

speed of first driver = (-b ± √(b^2 - 4ac)) / (2a)

where a = 1, b = -60, and c = 189.

Substituting the values:

speed of first driver = (-(-60) ± √((-60)^2 - 4(1)(189))) / (2(1))

speed of first driver = (60 ± √(3600 - 756)) / 2

speed of first driver = (60 ± √(2844)) / 2

speed of first driver = (60 ± 53.35) / 2

Taking the positive value:

speed of first driver = (60 + 53.35) / 2

speed of first driver = 113.35 / 2

speed of first driver = 56.675

Therefore, the speed of the first driver is approximately 56.675 km/h.

Answer

The speed of the first driver is approximately 56.675 km/h.