Question

Друг за другом по течению реки расположены три пристани: A, B и C. Катер стартует от пристани A, движется до C, очень быстро разворачивается и доходит до пристани B, как показано на рисунке 1. Путь занимает 45 минут. Затем катер возвращается обратно в A подобным образом: сначала движется от B до C, разворачивается и доходит до A (см. рисунок 2), затрачивая на 10 минут больше времени, чем в первом случае. Скорость течения реки и скорость лодки в стоячей воде равны: 1 м/с и 5 м/с. Перемещения поперёк реки занимают пренебрежимо малое время. Найти расстояние от А до С и от В до С

Answer 1

Ответ:

Ответ: АС=10800 м, ВС=3600 м.

Объяснение:

Пусть l1 расстояние между А и С, l2 расстояние между В и С. Vпо теч=1+5=6 м/с, Vпр теч=5-1=4 м/с. 45мин=2700 с, 55 мин=3300 с. Тогда {l1/6+l2/4=2700

{l1/4+l2/6=3300

Решаем систему АС=10800 м, ВС=3600 м.

Answer 2

Problem Analysis

We are given a scenario where a boat starts from dock A, travels to dock C, then quickly turns around and reaches dock B. The boat then returns to dock A by first traveling from dock B to dock C, turning around, and finally reaching dock A. We are asked to find the distance from A to C and from B to C.

Solution

To solve this problem, we need to consider the speed of the boat and the speed of the river current. Let's denote the speed of the boat in still water as v and the speed of the river current as c.

1. First, let's calculate the time it takes for the boat to travel from A to C and from B to C.

- From A to C: - The boat is traveling against the current, so the effective speed is v - c. - The distance from A to C is denoted as d_AC. - The time it takes to travel from A to C is given by the formula: time_AC = d_AC / (v - c).

- From B to C: - The boat is traveling with the current, so the effective speed is v + c. - The distance from B to C is denoted as d_BC. - The time it takes to travel from B to C is given by the formula: time_BC = d_BC / (v + c).

2. Next, let's calculate the time it takes for the boat to return from C to A.

- From C to A: - The boat is traveling against the current, so the effective speed is v - c. - The distance from C to A is the same as the distance from A to C, so d_CA = d_AC. - The time it takes to travel from C to A is given by the formula: time_CA = d_CA / (v - c).

3. Finally, let's calculate the total time it takes for the boat to complete the round trip.

- The total time is the sum of the time it takes to travel from A to C, the time it takes to travel from B to C, and the time it takes to travel from C to A: total_time = time_AC + time_BC + time_CA.

4. We are given that the total time is 45 minutes for the first trip and 10 minutes longer for the return trip. Therefore, we can set up the following equation:

- total_time = 45 minutes = time_AC + time_BC + time_CA - total_time + 10 minutes = time_AC + time_BC + time_CA

5. Now, we can solve the equations to find the values of d_AC and d_BC.

- Let's substitute the formulas for time_AC, time_BC, and time_CA into the equations: - 45 minutes = d_AC / (v - c) + d_BC / (v + c) + d_AC / (v - c) - 55 minutes = d_AC / (v - c) + d_BC / (v + c) + d_AC / (v - c)

- Simplifying the equations, we get: - 2 * d_AC / (v - c) + d_BC / (v + c) = 45 minutes - 2 * d_AC / (v - c) + d_BC / (v + c) = 55 minutes

- Rearranging the equations, we get: - 2 * d_AC * (v + c) + d_BC * (v - c) = 45 minutes * (v - c) * (v + c) - 2 * d_AC * (v + c) + d_BC * (v - c) = 55 minutes * (v - c) * (v + c)

- Since the distances d_AC and d_BC are the same in both equations, we can simplify further: - 2 * d_AC * (v + c) = 45 minutes * (v - c) * (v + c) - 2 * d_AC * (v + c) = 55 minutes * (v - c) * (v + c)

- Dividing both sides of the equations by (v + c), we get: - 2 * d_AC = 45 minutes * (v - c) - 2 * d_AC = 55 minutes * (v - c)

- Dividing both sides of the equations by 2, we get: - d_AC = 22.5 minutes * (v - c) - d_AC = 27.5 minutes * (v - c)

- Since the distances d_AC are the same in both equations, we can set them equal to each other: - 22.5 minutes * (v - c) = 27.5 minutes * (v - c)

- Dividing both sides of the equation by (v - c), we get: - 22.5 minutes = 27.5 minutes

- This equation is not possible, so there is no solution.

Conclusion

Based on the given information, it is not possible to determine the distance from A to C and from B to C. The calculations lead to an equation that is not possible, indicating that there is no solution.