Question

СРОЧНО!!!!Из города А в город В, расстояние между которыми 120км, выехали одновременно два велосипедиста. Скорость первого на 3 км/ч больше скорости воторого,поэтому он прибыл в город В на 2 ч раньше.Определите скорости велосипедистов.

Answer 1

Х-скорость медленного
х+3-скорость быстрого

120/х-120/(х+3)=2 
60/х-60/(х+3)=1  умножим х(х+3)
60(х+3)-60х=х(х+3)
60х+180-60х=х²+3х
180=х²+3х
х²+3х-180=0
D = 3² - 4·1·(-180) = 9 + 720 = 729
х=-15- не подходит
х=12км/ч-скорость медленного
12+3=15-скорость быстрого

Answer 2

Хкм/ч-скорость 2
х+3км/ч-скорость 1
120/х-120/(х+3)=2
2х²+6х-120(х+3-х)=0
2х²+6х-360=0
х²+3х-180=0
х1+х2=-3 и х1*х2=-180
х1=-15-не удов усл
х2=12км/ч-скорость 2
12+3=15км/ч-скорость 1

Answer 3

Problem Analysis

We have two cyclists traveling from City A to City B, a distance of 120 km. The first cyclist's speed is 3 km/h faster than the second cyclist's speed. As a result, the first cyclist arrives in City B 2 hours earlier than the second cyclist. We need to determine the speeds of both cyclists.

Solution

Let's assume the speed of the second cyclist is x km/h. Therefore, the speed of the first cyclist is x + 3 km/h.

We can use the formula time = distance / speed to calculate the time taken by each cyclist to travel from City A to City B.

For the first cyclist: - Distance = 120 km - Speed = x + 3 km/h - Time = 120 / (x + 3) hours

For the second cyclist: - Distance = 120 km - Speed = x km/h - Time = 120 / x hours

According to the problem, the first cyclist arrives in City B 2 hours earlier than the second cyclist. Therefore, we can set up the following equation:

120 / (x + 3) = 120 / x + 2

Now, let's solve this equation to find the value of x.

Calculation

To solve the equation, we can cross-multiply and simplify:

120x = 120(x + 3) + 2x(x + 3)

120x = 120x + 360 + 2x^2 + 6x

Rearranging the terms:

0 = 2x^2 + 6x + 360

Dividing the equation by 2:

0 = x^2 + 3x + 180

Now, we can solve this quadratic equation using the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 1, b = 3, and c = 180.

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

Discriminant = 3^2 - 4(1)(180) = 9 - 720 = -711

Since the discriminant is negative, the quadratic equation has no real solutions. This means there is no valid solution for the speeds of the cyclists that satisfies the given conditions.

Answer

There is no valid solution for the speeds of the two cyclists that satisfies the given conditions.