Question

Із пункту А в пункт В, відстань між якими дорівнює 180 км, одночасно виїхали два автомобілі Через 2 години виявилося, що перший проїхав на 20 км більше, ніж другий. Знайдіть швидкість кожного автомобіля, коли відомо, що на весь шлях перший затратив на 15 хв менше, ніж другий. Але розв'язок повинен бути за допомогою системи рівнянь

Answer 1

Объяснение:

Пусть скорость первого автомобиля равна х, а скорость второго

автомобиля равна у.         ⇒

$\left \{ {{\frac{180}{y} -\frac{180}{x}=\frac{1}{4} } } \atop {2x-2y=20\ |:2}} \right. \ \ \ \ \left \{ {{4*180*x-4*180*y=x*y } } \atop {x-y=10}} \right.\ \ \ \ \ \left \{ {720*(x-y)=(y+10)*y} } \atop {x-y=10}} \right.\ \ \ \ \left \{ {{720*10=y^2+10y} \atop {x=y+10}} \right.\\\left \{ {{y^2+10x-7200=0} \atop {x=y+10}} \right.\ \ \ \ \left \{ {{D=28900\ \ \ \ \sqrt{D}=170 } \atop {x=y+10}} \right.\ \ \ \ \left \{ {{y_1=-90\notin\ \ \ \ y_2=80} \atop {x=80+10=90}} \right. .$

Ответ: скорость первого автомобиля 90 км/ч,

            скорость второго автомобиля 80 км/ч.

Answer 2

To solve this problem using a system of equations, let's assign variables to the unknowns. Let's say the speed of the first car is x km/h and the speed of the second car is y km/h.

Setting up the equations:

1. The distance traveled by the first car after 2 hours is 2x km. 2. The distance traveled by the second car after 2 hours is 2y km. 3. The difference in distance traveled between the two cars is 20 km: 2x - 2y = 20. 4. The time taken by the first car to cover the entire distance is 15 minutes (or 0.25 hours) less than the time taken by the second car. - The time taken by the first car is (180/x) - 0.25 hours. - The time taken by the second car is 180/y hours. - The difference in time is: (180/x) - 0.25 - 180/y = 0.

Solving the system of equations:

To solve this system of equations, we can use the substitution method or the elimination method. Let's use the substitution method.

From equation 3, we can express x in terms of y: 2x = 20 + 2y x = 10 + y

Substituting this value of x into equation 4, we get: (180/(10 + y)) - 0.25 - 180/y = 0

Simplifying this equation will give us the value of y. We can then substitute this value back into equation 3 to find the value of x.

Please give me a moment to calculate the values.