Question

Из пункта A в пункт B, расстояние между которыми 45 км. выехал велосипедист.Через 30 мин вслед за ним выехал второй велосипедист, который прибыл в пункт B на 15 мин раньше первого.Какова скорость первого велосипедиста, если она на 3 км/ч. меньше скорости второго.

Answer 1

пусть х скорость первого велосипедиста тогда скорость второго x+3 зная что второму понадобилось на 30+15=45 мин=3/4часа меньше составим и решим уравнение

45/x-45/x+3=3/4

45*4*(x+3)-45*4*x-3*x(x+3)=0

180x+540-180x-3xво второй степени-9ч=0

-3xво2-9x+540=0/-3

xво2+3x-180=0

D=9+720=729

x=-3+27/2=12

x=-3-27/2неподходит по смыслу задачи

ответ:12км/ч

Answer 2

Problem Analysis

We are given that a cyclist travels from point A to point B, a distance of 45 km. Another cyclist follows the first cyclist after 30 minutes and arrives at point B 15 minutes before the first cyclist. We need to find the speed of the first cyclist, given that it is 3 km/h slower than the speed of the second cyclist.

Solution

Let's assume the speed of the first cyclist is x km/h. Since the second cyclist is 3 km/h faster, their speed is x + 3 km/h.

We can use the formula speed = distance / time to calculate the time taken by each cyclist to travel from A to B.

The first cyclist takes 45 / x hours to travel from A to B.

The second cyclist takes 45 / (x + 3) hours to travel from A to B.

According to the problem, the second cyclist arrives 15 minutes (or 0.25 hours) before the first cyclist. So, the time taken by the second cyclist is 30 minutes (or 0.5 hours) less than the time taken by the first cyclist.

Setting up the equation: 45 / (x + 3) = 45 / x - 0.5

To solve this equation, we can cross-multiply and simplify:

45x = 45(x + 3) - 0.5x(x + 3)

Simplifying further:

45x = 45x + 135 - 0.5x^2 - 1.5x

Combining like terms:

0 = -0.5x^2 - 1.5x + 135

Now, we can solve this quadratic equation to find the value of x.

Quadratic Equation Solution

Using the quadratic formula x = (-b ± √(b^2 - 4ac)) / (2a), where a = -0.5, b = -1.5, and c = 135:

x = (-(-1.5) ± √((-1.5)^2 - 4(-0.5)(135))) / (2(-0.5))

Simplifying:

x = (1.5 ± √(2.25 + 270)) / (-1)

x = (1.5 ± √(272.25)) / (-1)

x = (1.5 ± 16.5) / (-1)

So, we have two possible values for x:

x = (1.5 + 16.5) / (-1) = 18 / (-1) = -18

x = (1.5 - 16.5) / (-1) = -15 / (-1) = 15

Since speed cannot be negative, we can discard the negative value of x.

Therefore, the speed of the first cyclist is 15 km/h.

Answer

The speed of the first cyclist is 15 km/h.