Question

Из пункта А в пункт В, расстояние между которыми равно 180км. одновременно выехали два автомобиля. Через 2 часа оказалось, что первый проехал на 20 км больше, чем второй. Найдите скорость каждого автомобиля, когда известно, что на весь путь первый затратил на 15 мин меньше, чем второй.

Answer 1

Пусть x-скорость первого, y-cкорость второго.

Составим таблицу:

 

Формула:

U=S/T

 

                                U(км/ч)       S(км)        T(ч)

1 авто(весь путь)      x                180           180/x

 

         (часть пути)     x                 2x             2

 

2 авто(весь путь)      y                 180           180/y

 

         (часть пути)     y                  2y             2

 

 

 

Составим систему:

2x+20=2y

180/x=180/y+1/4(1/4ч=15 мин)

 

2x=2y-20

720y=720x+xy

 

x=(2y-20)/2

720y=720x+xy

 

 

Подставляем:

720y=720(y-10)+(y-10)y

y^2-10y-7200=0

D=100+4*7200=28900

Корень из Dискриминанта=170

x1=(10+170)/2=90км/ч-скорость первого.

x2-не подходит т.к.скорость не может быть отриц. числом

 

Найдём S второго:

подставляем 2*90=2y-20

200=2y

y=100км/ч

Oтвет:90км/x, 100км/ч.

 

 

 

Answer 2

Problem Analysis

We have two cars traveling from point A to point B, a distance of 180 km. The first car traveled 20 km more than the second car after 2 hours. We need to find the speed of each car given that the first car took 15 minutes less than the second car to complete the entire journey.

Solution

Let's assume the speed of the first car is v1 km/h and the speed of the second car is v2 km/h.

We know that the distance traveled by the first car after 2 hours is 20 km more than the distance traveled by the second car. Therefore, we can write the equation:

Distance traveled by the first car after 2 hours = Distance traveled by the second car after 2 hours + 20 km

Using the formula Distance = Speed × Time, we can write the equation:

v1 × 2 = v2 × 2 + 20

Simplifying the equation, we get:

2v1 - 2v2 = 20 ---(Equation 1)

We also know that the first car took 15 minutes less than the second car to complete the entire journey. Since the time taken by the second car is the total time minus 15 minutes, we can write the equation:

180/v1 = (180/v2) - 15/60

Simplifying the equation, we get:

180v2 - 15v1 = 180v1

Simplifying further, we get:

180v2 - 195v1 = 0 ---(Equation 2)

We now have a system of two equations with two variables (Equation 1 and Equation 2). We can solve this system of equations to find the values of v1 and v2.

Solving the System of Equations

To solve the system of equations, we can use the substitution method. We'll solve Equation 1 for v1 and substitute it into Equation 2.

From Equation 1, we have:

v1 = v2 + 10 ---(Equation 3)

Substituting Equation 3 into Equation 2, we get:

180v2 - 195(v2 + 10) = 0

Simplifying the equation, we get:

180v2 - 195v2 - 1950 = 0

Combining like terms, we get:

-15v2 - 1950 = 0

Simplifying further, we get:

-15v2 = 1950

Dividing both sides by -15, we get:

v2 = -130

Since the speed cannot be negative, we discard this solution.

Therefore, there is no valid solution for the given problem.

Conclusion

Based on the given information, there is no valid solution for the problem of finding the speeds of the two cars.