Question

5. Если автомобиль из пункта А в пункт В будет ехать со скоростью 80 км/ч, то он опоздает на 30 мин, а если будет ехать со скоростью 90 км/ч, то приедет раньше на 10 мин. Найдите расстояние между пунктами А и В.

Answer 1

Пусть х расстояние между пунктами А и В, t заданное время прибытия, тогда при скорости 80 км/ч  t=х/80-1/2  или при скорости 90 км/ч t=х/90+1/6    так как t=t  
х/80-1/2=х/90+1/6     х/80-х/90=1/6+1/2   (9*х-8*х)/720 =4/6   х/720=2/3
х=720*2/3=480 км расстояние между пунктами А и В.

Answer 2

Finding the Distance between Points A and B

To find the distance between points A and B, we can use the given information about the time it takes to travel at different speeds. Let's calculate the distance using the given data.

Given: - Speed at 80 km/h: Delay of 30 minutes - Speed at 90 km/h: Arrival 10 minutes early

To calculate the distance, we can set up a system of equations based on the time and speed relationships.

Let's assume the distance between points A and B is represented by d.

Equation 1: d/80 = t + 30 (where t is the time taken to travel at 80 km/h) Equation 2: d/90 = t - 10 (where t is the time taken to travel at 90 km/h)

To solve this system of equations, we can use substitution or elimination.

Let's use substitution to solve the system of equations:

From Equation 1, we can express t in terms of d: t = (d/80) - 30

Substituting this value of t into Equation 2: (d/90) = ((d/80) - 30) - 10

Simplifying the equation: d/90 = (d/80) - 40

To solve for d, we can multiply both sides of the equation by the least common multiple (LCM) of 80 and 90, which is 720:

720 * (d/90) = 720 * ((d/80) - 40)

Simplifying further: 8d = 9d - 28800

Solving for d: d = 28800

Therefore, the distance between points A and B is 28800 km.

Note: The given information does not specify the units of distance, so we assume it is in kilometers.