Question

СРОЧНО ПОМОЖІТЬ З ДЗ ДАЮ 50 БАЛОВ ЗА 1 ЗАДАЧУ 1) З міста А в місто В відстань між якими 420 км одночасно виїхали два легковики. Швидкість одного з них на 10 км/год більша за швидкість другого і тому він пробув у місто В на 1 год раніше ніж другий. Знайдіть швидкість кожного з легковиків.

Answer 1

Ответ:

70; 60

Объяснение:

(x+10) - скорость 1-й легковушки, км/ч.

x - скорость 2-й легковушки, км/ч.

420/x -420/(x+10)=1

420(x+10-x)=x(x+10)

x²+10x-4200=0; D=100+16800=16900

x₁=(-10-130)/2=-140/2=-70 - ответ не подходит.

x₂=(-10+130)/2=120/2=60 км/ч - скорость 2-й легковушки.

60+10=70 км/ч - скорость 1-й легковушки.

Answer 2

Ответ:

70 км/ч и 60 км/ч

Объяснение:

пусть скорость одной машины х км/ч, другой у км/ч, тогда

 х-у=10⇒х=10+у

а время связано условием с.о.:

420/у-420/х=1

приведем к общем знаменателю.

420(х-у)=ху

подставим вместо х-у число 10, а вместо х в правой части 10+у

получим 400=у*(10+у)

у²+10у-4200=0

по теореме, обратной теореме Виета, корни равны -70  не подходит по смыслу задачи. и  у=60

значит, скорость второй машины 60 км/ч, тогда скорость первой

60+10=70 (км/ч )

Answer 3

Problem Analysis

To solve this problem, we need to find the speeds of two cars that traveled from city A to city B. We are given that the distance between the cities is 420 km and that one car arrived in city B one hour earlier than the other car. Additionally, we know that the speed of one car is 10 km/h greater than the speed of the other car.

Solution

Let's assume the speed of the slower car is x km/h. Therefore, the speed of the faster car will be x + 10 km/h.

We can use the formula distance = speed × time to calculate the time taken by each car to travel from city A to city B.

For the slower car: - Distance = 420 km - Speed = x km/h - Time = 420 / x hours

For the faster car: - Distance = 420 km - Speed = x + 10 km/h - Time = 420 / (x + 10) hours

According to the problem, the faster car arrived in city B one hour earlier than the slower car. Therefore, we can set up the following equation:

420 / x - 420 / (x + 10) = 1

To solve this equation, we can multiply both sides by x(x + 10) to eliminate the denominators:

420(x + 10) - 420x = x(x + 10)

Simplifying the equation:

420x + 4200 - 420x = x^2 + 10x

4200 = x^2 + 10x

Rearranging the equation:

x^2 + 10x - 4200 = 0

Now we can solve this quadratic equation to find the value of x.

Quadratic Equation Solution

Using the quadratic formula x = (-b ± √(b^2 - 4ac)) / (2a), where a = 1, b = 10, and c = -4200, we can find the values of x.

Calculating the discriminant (b^2 - 4ac):

D = (10^2) - 4(1)(-4200) = 100 + 16800 = 16900

Since the discriminant is positive, we have two real solutions for x.

Calculating the solutions:

x = (-10 + √16900) / 2 = (-10 + 130) / 2 = 120 / 2 = 60

x = (-10 - √16900) / 2 = (-10 - 130) / 2 = -140 / 2 = -70

Since the speed of a car cannot be negative, we discard the solution x = -70.

Therefore, the speed of the slower car is 60 km/h and the speed of the faster car is 60 + 10 = 70 km/h.

Answer

The speed of the slower car is 60 km/h and the speed of the faster car is 70 km/h.