Question

расстояние в 60 км петя проехал на велосипеде на 1 час быстрее васи .найти их скорости,если скорость пети на 3 км/ч больше.

Answer 1

Х км\ч -скорость Пети, (х-3) км\ч-скорость Васи.
60\х+ 1=60\(х-3), \*х (х-3),
60х+х (х-3)=60х,
х^2-3х-180=0,
х1=15, х2=-12(не уд. усл) 15 км\ч-скор. Пети, 12 км\ч-скорость Васи.

Answer 2

Problem Analysis

We are given that Petya traveled a distance of 60 km on a bicycle in 1 hour less time than Vasya. We are also told that Petya's speed is 3 km/h faster than Vasya's speed. We need to find the speeds of both Petya and Vasya.

Solution

Let's assume that Vasya's speed is x km/h. Since Petya's speed is 3 km/h faster, Petya's speed will be x + 3 km/h.

We know that distance = speed × time.

For Vasya, the distance he traveled is 60 km and the time taken is t hours (which is the time taken by Petya minus 1 hour). So, we have the equation:

60 = x × t For Petya, the distance he traveled is also 60 km and the time taken is t - 1 hours. So, we have the equation:

60 = (x + 3) × (t - 1) We can solve these two equations to find the values of x and t.

Solving the Equations

Let's solve the equations and to find the values of x and t.

From equation we can express t in terms of x:

t = 60 / x Substituting equation into equation we get:

60 = (x + 3) × (60 / x - 1)

Simplifying this equation, we have:

60 = (x + 3) × (60 - x) / x

Cross-multiplying, we get:

60x = (x + 3) × (60 - x)

Expanding the equation, we have:

60x = 60x - x^2 + 180 - 3x

Simplifying further, we get:

0 = -x^2 + 180 - 3x

Rearranging the terms, we have:

x^2 - 3x - 180 = 0

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

Solving the Quadratic Equation

We can solve the quadratic equation x^2 - 3x - 180 = 0 using the quadratic formula:

x = (-b ± sqrt(b^2 - 4ac)) / (2a)

For our equation, a = 1, b = -3, and c = -180.

Substituting these values into the quadratic formula, we get:

x = (-(-3) ± sqrt((-3)^2 - 4(1)(-180))) / (2(1))

Simplifying further, we have:

x = (3 ± sqrt(9 + 720)) / 2

x = (3 ± sqrt(729)) / 2

x = (3 ± 27) / 2

So, we have two possible values for x:

x = (3 + 27) / 2 = 30 x = (3 - 27) / 2 = -12 Since speed cannot be negative, we can discard the value of x = -12.

Therefore, the speed of Vasya is x = 30 km/h.

Now, we can substitute this value of x into equation to find the value of t:

t = 60 / x = 60 / 30 = 2 So, the time taken by Vasya is t = 2 hours.

Finally, we can calculate Petya's speed by adding 3 km/h to Vasya's speed:

Petya's speed = Vasya's speed + 3 = 30 + 3 = 33 km/h.

Answer

Therefore, the speed of Vasya is 30 km/h and the speed of Petya is 33 km/h.

Let me know if you need any further assistance!