Question

Расстояние между пунктами А и В автомобиль проехал за 0,5часа,а велосипидист за 3,5часа.Найдите скорость каждого,если автомобиль двигался на 60 км в час быстрее,чем велосипедист?

Answer 1

Пусть х - скорость автомобиля, у - скорость велосипедиста. Расстояние между А и В велосипедист проехал со скоростью у за 3,5 часа, автомобиль же проехал со скоростью х за 0,5 часа:

0,5х = 3,5у;  х = 7у

Скорость автомобиля выше скорости велосипедиста на 60 км/ч:

x = y + 60

Решаем систему:

$\left \{ {{x = 7y} \atop {x = y + 60}} \right. \\ \\ 7y = y + 60 \\ 6y = 60 \\ \\ y=10 \\ x = 7*10 = 70$

Ответ: 10 км/ч велосипедист; 70 км/ч автомобиль

Answer 2

Calculation of Speed

To find the speed of the car and the cyclist, we can use the formula:

Speed = Distance / Time

Given that the car traveled the distance between points A and B in 0.5 hours, and the cyclist took 3.5 hours, we can calculate their speeds.

Let's assume the speed of the cyclist is x km/h. Since the car is traveling 60 km/h faster than the cyclist, the speed of the car would be x + 60 km/h.

Using the formula mentioned above, we can calculate the distances traveled by the car and the cyclist.

The distance traveled by the car can be calculated as:

Distance_car = Speed_car * Time_car

Substituting the values, we get:

Distance_car = (x + 60) * 0.5

Similarly, the distance traveled by the cyclist can be calculated as:

Distance_cyclist = Speed_cyclist * Time_cyclist

Substituting the values, we get:

Distance_cyclist = x * 3.5

Since the distances traveled by both the car and the cyclist are the same (as they are traveling between the same points), we can equate the two equations:

(x + 60) * 0.5 = x * 3.5

Simplifying the equation:

0.5x + 30 = 3.5x

30 = 3x

x = 10

Therefore, the speed of the cyclist is 10 km/h and the speed of the car is 70 km/h.