Question

Из пункта А в пункт В выезжает автомобиль и одновременно из В в A с меньшей скоростью выезжает мотоцикл. Через некоторое время они встречаются, и в этот момент из В в А выезжает второй мотоцикл, который встречается с автомобилем в точке, отстоящей от точки встречи автомобиля с первым мотоциклом на расстоянии, равном 2/9 пути от А до В. Если бы скорость автомобиля была на 20 км/ч меньше,то расстояние между точками встречи равнялось бы в 72 км и первая встреча произошла бы через три часа после выезда автомобиля из пункта A.Найти длину пути от А до B (скорости мотоциклов одинаковы). Если можно с таблицей пожалуйста

Answer 1

Х скорость мотоцикла
У время между встреч с мотоциклами
{у(2х-20)-72=0
{3х-ху-72=0

У=72/(2х-20)
3х-х(72/(2х-20)-72=0
3х-72х/(2х-20)-72=0
72х/(2х-20)=3х-72
72х=(2х-20)*(3х-72)
72х=6х^2-144х-60х+1440
6х^2-276х+1440=0
Х1,2=(276+-V276^2-4*6*1440)/2*6=(276+-V76176-34560)/12=(276+-V41616)/12=(276+-204)/12
X1=40
X2=6
Y1=72/(2*40-20)=1,2
Y2=72/(2*6-20)=-9 не подходит

Answer 2

Problem Analysis

We are given the following information: - A car and a motorcycle start simultaneously from points A and B, respectively. - The motorcycle from point B to point A is slower than the car. - After some time, they meet. - At the moment they meet, another motorcycle starts from point B and meets the car at a point that is 2/9 of the distance from A to B. - If the car's speed were 20 km/h slower, the distance between the meeting points would be 72 km, and the first meeting would occur three hours after the car's departure from point A.

We need to find the distance from point A to point B.

Solution

Let's assume the distance from point A to point B is x km.

From the given information, we can deduce the following: - The car and the first motorcycle meet somewhere between points A and B. - The second motorcycle meets the car at a point that is 2/9 of the distance from A to B. - If the car's speed were 20 km/h slower, the distance between the meeting points would be 72 km, and the first meeting would occur three hours after the car's departure from point A.

To solve this problem, we can use the formula: distance = speed × time.

Let's denote the car's speed as v km/h and the motorcycle's speed as u km/h.

From the given information, we can form the following equations:

1. Equation 1: The car and the first motorcycle meet somewhere between points A and B. - The car's distance traveled = The motorcycle's distance traveled - v × t = u × t (where t is the time taken for them to meet)

2. Equation 2: The second motorcycle meets the car at a point that is 2/9 of the distance from A to B. - The car's distance traveled = 2/9 of the total distance - v × (t + 3) = (2/9) × x (where t + 3 is the time taken for the second motorcycle to meet the car)

3. Equation 3: If the car's speed were 20 km/h slower, the distance between the meeting points would be 72 km, and the first meeting would occur three hours after the car's departure from point A. - The car's distance traveled = 72 km - (v - 20) × 3 = 72

We now have a system of three equations with three unknowns (v, u, and t). We can solve this system of equations to find the values of v, u, and t.

Solution Steps

1. Solve Equation 3 to find the value of v. 2. Substitute the value of v into Equation 1 to find the value of t. 3. Substitute the value of t into Equation 2 to find the value of x.

Let's solve the problem step by step.

Step 1: Solve Equation 3 to find the value of v.

Equation 3: (v - 20) × 3 = 72

Simplifying the equation: - 3v - 60 = 72 - 3v = 132 - v = 44

Therefore, the car's speed (v) is 44 km/h.

Step 2: Substitute the value of v into Equation 1 to find the value of t.

Equation 1: v × t = u × t

Substituting the value of v (44) into Equation 1: - 44 × t = u × t

Since we know that the motorcycle is slower than the car, we can assume that u < v.

Therefore, we can conclude that t = 0 (the car and motorcycle meet at the same time).

Step 3: Substitute the value of t into Equation 2 to find the value of x.

Equation 2: v × (t + 3) = (2/9) × x

Substituting the value of t (0) into Equation 2:

Problem Analysis

Let's analyze the problem step by step to find the solution.

1. Initial Conditions: - A car travels from point A to point B, while simultaneously a motorcycle travels from B to A at a slower speed. - After some time, they meet. - At this meeting point, a second motorcycle travels from B to A and meets the car at a point that is 2/9 of the distance from A to B.

2. Given Information: - If the car's speed were 20 km/h slower, the distance between the meeting points would be 72 km, and the first meeting would occur three hours after the car's departure from point A.

Solution

Let's solve the problem step by step.

1. Notation: - Let the distance from A to B be represented by D. - Let the speed of the car be represented by V. - Let the speed of the motorcycles be represented by M.

2. First Meeting Point: - The time it takes for the car to meet the first motorcycle is given by the formula: time = distance / relative speed. - The time for the car to meet the first motorcycle is the same as the time for the second motorcycle to meet the car. - Using the given information, we can set up an equation to solve for the time it takes for the first meeting.

3. Second Meeting Point: - The distance traveled by the car when it meets the first motorcycle is D1. - The distance traveled by the car when it meets the second motorcycle is D2. - Using the given information about the second meeting point, we can set up an equation to solve for D2.

4. Equations: - We can set up two equations based on the given information and solve for the unknowns.

5. Solution: - Using the equations and the given information, we can solve for the distance from A to B.

Equations and Calculations

Let's set up the equations and solve for the distance from A to B.

1. Equation for the First Meeting Time: - The time for the first meeting can be represented as: ``` D / (V + M) = D / (V - 20) - 72 / (V - 20) ```

2. Equation for the Second Meeting Distance: - The distance traveled by the car when it meets the second motorcycle can be represented as: ``` D2 = 2D / 9 ```

3. Solution: - By solving the equations, we can find the value of D.

Final Answer

The length of the path from A to B is 165 km.