Question

Из пункта А в пункт В, расстояние между которыми 60 км, одновременно выехали автомобилист и велосипедист. Известно, что в час автомобилист проезжает на 50 км больше, чем велосипедист. Определите скорость велосипедиста, если известно, что он прибыл в пункт В на 5 часов позже автомобилиста. Ответ дайте в км/ч.

Answer 1

10км/ч
Если нужно объяснение проси.

Answer 2

Problem Analysis

We are given that an automobile and a cyclist simultaneously traveled from point A to point B, which are 60 km apart. The automobile travels 50 km/h faster than the cyclist. We need to determine the speed of the cyclist if we know that the cyclist arrived at point B 5 hours after the automobile.

Solution

Let's assume the speed of the cyclist is x km/h. Since the automobile travels 50 km/h faster, its speed is x + 50 km/h.

We can use the formula distance = speed × time to set up two equations:

1. For the automobile: 60 = (x + 50) × t (where t is the time in hours) 2. For the cyclist: 60 = x × (t + 5)

We can solve this system of equations to find the value of x.

Solution Steps

1. Substitute 60 for the distance in both equations. 2. Simplify the equations. 3. Solve the system of equations to find the value of x.

Let's solve the system of equations step by step.

Equation 1: Automobile

The equation for the automobile is 60 = (x + 50) × t.

Equation 2: Cyclist

The equation for the cyclist is 60 = x × (t + 5).

Solving the System of Equations

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

From Equation 2, we have:

60 = x × (t + 5)

Simplifying, we get:

60 = xt + 5x

Rearranging, we get:

xt = 60 - 5x

Now, substitute this value of xt into Equation 1:

60 = (x + 50) × t

Substituting 60 - 5x for xt, we get:

60 = (x + 50) × (60 - 5x)

Expanding and simplifying, we get:

60 = 60x + 3000 - 5x^2 - 250x

Rearranging, we get:

5x^2 + 310x + 3000 - 60 = 0

Simplifying further, we get:

5x^2 + 310x - 3060 = 0

Now, we can solve this quadratic equation using the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, a = 5, b = 310, and c = -3060.

Substituting these values into the quadratic formula, we get:

x = (-310 ± √(310^2 - 4 * 5 * -3060)) / (2 * 5)

Simplifying further, we get:

x = (-310 ± √(96100 + 61200)) / 10

x = (-310 ± √(157300)) / 10

x = (-310 ± 397.12) / 10

Now, we have two possible values for x:

1. x = (-310 + 397.12) / 10 2. x = (-310 - 397.12) / 10

Calculating these values, we get:

1. x = 8.712 2. x = -70.712

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

Therefore, the speed of the cyclist is approximately 8.712 km/h.

Answer

The speed of the cyclist is approximately 8.712 km/h.