Question

На 80 км пути велосипедист тратит на 2 ч больше, чем мотоциклист, так как его скорость на 20 км/ч меньше.Найдите скорость велосипедиста.(черех "пусть х..")

Answer 1

пусть x - скорость велосипедиста, тогда скорость мотоциклиста (x+20)

    80/x - 80/(x+20)=2

    80(x+20)-80x=2x(x+20)

    80x+1600-80x=2x^2+40x

    2x^2+40x-1600=0

    x^2+20x-800=0

  D=3600

   x1=-40 - не удовлетворяет ОДЗ

   x2=20 - скорость велосипедиста

 

Answer 2

Problem Analysis

We are given that a cyclist takes 2 hours longer than a motorcyclist to cover a distance of 80 km. The reason for this is that the cyclist's speed is 20 km/h slower than the motorcyclist's speed. We need to find the speed of the cyclist.

Solution

Let's assume the speed of the motorcyclist is x km/h. According to the problem, the cyclist's speed is 20 km/h slower, so the cyclist's speed is x - 20 km/h.

We can use the formula time = distance / speed to calculate the time taken by each of them.

The time taken by the motorcyclist to cover 80 km is: time_motorcyclist = 80 / x hours

The time taken by the cyclist to cover 80 km is: time_cyclist = 80 / (x - 20) hours

We are given that the cyclist takes 2 hours longer than the motorcyclist, so we can set up the equation:

time_cyclist = time_motorcyclist + 2

Substituting the values of time_cyclist and time_motorcyclist, we get:

80 / (x - 20) = 80 / x + 2

To solve this equation, we can cross-multiply:

80x = 80(x - 20) + 2x(x - 20)

Simplifying the equation:

80x = 80x - 1600 + 2x^2 - 40x

Combining like terms:

0 = 2x^2 - 40x - 1600

Dividing the equation by 2 to simplify:

0 = x^2 - 20x - 800

Now we have a quadratic equation. We can solve it by factoring or using the quadratic formula. Let's use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, a = 1, b = -20, and c = -800. Substituting these values into the formula:

x = (-(-20) ± √((-20)^2 - 4(1)(-800))) / (2(1))

Simplifying:

x = (20 ± √(400 + 3200)) / 2

x = (20 ± √3600) / 2

x = (20 ± 60) / 2

We have two possible solutions:

x1 = (20 + 60) / 2 = 80 / 2 = 40

x2 = (20 - 60) / 2 = -40 / 2 = -20

Since speed cannot be negative, we discard the negative solution. Therefore, the speed of the motorcyclist is 40 km/h.

The speed of the cyclist is x - 20 = 40 - 20 = 20 km/h.

Answer

The speed of the cyclist is 20 km/h.