Question

Из пункта А в пункт В,расстояние между которыми 60 км,одновременно выехали велосипедист и мотоциклист.Известно,что за час мотоциклист проезжает на 40 км больше,чем велосипедист.Определите скорость велосипедиста,если он прибыл в пункт В на 2 часа позже мотоциклиста.Ответ дайте в км/ч!!!!! Срочно!!!!

Answer 1

Хкм/ч скорость велосипедиста,х+40км/ч скорость мотоциклиста
60/х-60/(х+40)=2
2х²+80х-60(х+40-х)=0
2х²+80х-2400=0
х²+40х-1200=0
х1+х2=-40 и х1*х2=-1200
х1=-60 не удов усл
х2=20км/ч скорость велосипедиста

Answer 2

Problem Analysis

We are given that a cyclist and a motorcyclist simultaneously start from point A and point B, which are 60 km apart. The motorcyclist travels 40 km more than the cyclist in one hour. The cyclist arrives at point B two hours after the motorcyclist. We need to determine the speed of the cyclist in km/h.

Solution

Let's assume the speed of the cyclist is x km/h. Since the motorcyclist travels 40 km more than the cyclist in one hour, the speed of the motorcyclist is x + 40 km/h.

We can use the formula distance = speed × time to solve this problem. The time taken by the cyclist to travel from point A to point B is 60 / x hours, and the time taken by the motorcyclist is 60 / (x + 40) hours.

According to the given information, the cyclist arrives at point B two hours after the motorcyclist. Therefore, we can set up the equation:

60 / x = 60 / (x + 40) + 2

To solve this equation, we can multiply both sides by x(x + 40) to eliminate the denominators:

60(x + 40) = 60x + 2x(x + 40)

Simplifying the equation:

60x + 2400 = 60x + 2x^2 + 80x

Combining like terms:

2x^2 + 140x - 2400 = 0

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)

In this equation, a = 2, b = 140, and c = -2400. Plugging in these values:

x = (-140 ± √(140^2 - 4 * 2 * -2400)) / (2 * 2)

Simplifying further:

x = (-140 ± √(19600 + 19200)) / 4

x = (-140 ± √38800) / 4

x = (-140 ± 196.99) / 4

Now we have two possible values for x. Let's calculate them:

x1 = (-140 + 196.99) / 4 ≈ 14.75

x2 = (-140 - 196.99) / 4 ≈ -84.75

Since speed cannot be negative, we can discard the negative value of x. Therefore, the speed of the cyclist is approximately 14.75 km/h.

Answer

The speed of the cyclist is approximately 14.75 km/h.