Question

Из пункта А в пункт В, расстояние между которыми 60 км, одновременно выехали автомобилист и велосипедист. Известно, что в час автомобилист проезжает на 35 км больше, чем велосипедист. Определите скорость велосипедиста, если известно, что он прибыл в пункт В на 2ч 48мин. позже автомобилиста. Ответ дайте в км/ч

Answer 1

Х км/ч - скорость вело. (х+35) км/ч - скорость авто.
$\frac{60}{x}$ ч - тратит на путь вело.
$\frac{60}{x+35}$ ч - тратит на путь авто.
Разница 2ч48мин=$2 \frac{48}{60} =2 \frac{4}{5}$ ч
$\frac{60}{x}-\frac{60}{x+35}=2\frac{4}{5} \\ \frac{60}{x}-\frac{60}{x+35}=\frac{14}{5} \\ \frac{30}{x}-\frac{30}{x+35}=\frac{7}{5} \\ \pi pu\ x \neq 0,x \neq -35 =\ \textgreater \ 150x+5250-150x=7x^2+245x \\ 7x^2+245x-5250=0 \\ x^2 +35x -750=0\\ D=35^2+3000 = 4225=65^2$
$x= \frac{-35 \pm 65}{2}\\ x_1=-50,\ x_2=15$
Исходя из смысла величин задачи, берем х=15 км/ч - скорость вело, тогда
15+35=50 км/ч - скорость авто.
Ответ: 15 км/ч.

Answer 2

Problem Analysis

We are given that a car and a cyclist simultaneously left point A and are traveling towards point B, which is 60 km away. It is known that the car travels 35 km/h faster than the cyclist. We need to determine the speed of the cyclist if they arrived at point B 2 hours and 48 minutes later than the car.

Solution

Let's assume the speed of the cyclist is x km/h. Since the car travels 35 km/h faster than the cyclist, the speed of the car is x + 35 km/h.

To find the time it takes for each to reach point B, we can use the formula: time = distance / speed.

The time taken by the cyclist to reach point B is given as 2 hours and 48 minutes, which is equivalent to 2.8 hours.

Using the formula, we can calculate the time taken by the cyclist and the car as follows:

For the cyclist: time = distance / speed 2.8 = 60 / x

For the car: time = distance / speed 2.8 = 60 / (x + 35)

Now we can solve these two equations to find the value of x, which represents the speed of the cyclist.

Calculation

Let's solve the equations:

From the equation 2.8 = 60 / x, we can cross-multiply to get: 2.8x = 60

Dividing both sides by 2.8, we get: x = 60 / 2.8

Using a calculator, we find that x ≈ 21.43 km/h.

Therefore, the speed of the cyclist is approximately 21.43 km/h.

Answer

The speed of the cyclist is approximately 21.43 km/h.