Question

Теплоход проходит некоторое расстояние по течению реки за 2ч.,к против -за 3ч. За сколько часов это же расстояние пройдет плот ? Напишите решение. Должно получиться 12

Answer 1

Пусть  1 - это данное расстояние
1/2 - скорость теплохода по течению 
1/3 - скорость теплохода против течения 
х - скорость течения реки, это же скорость плота 
(1/2 - х) - собственная скорость теплохода в стоячей воде 
(1/3 + х) - собственная скорость теплохода в стоячей воде 
Уравнение 
1/2 - х = 1/3 + х
х + х =  1/2 - 1/3
2х = 1/6
х = 1/6  : 2
х = 1/12  - скорость течения реки, это же скорость плота 
А теперь расстояние, равное 1, делим на скорость 1/12 и получаем искомое время плота
1 : 1/12 = 12 часов
Ответ: 12 часов

Answer 2

Problem Analysis

The problem states that a boat travels a certain distance downstream in 2 hours and the same distance upstream in 3 hours. We need to find out how long it will take for a raft to cover the same distance.

Solution

Let's denote the speed of the boat as b and the speed of the river current as c. The speed of the boat downstream is the sum of the speed of the boat and the speed of the current, and the speed of the boat upstream is the difference between the speed of the boat and the speed of the current.

Given: - Time downstream = 2 hours - Time upstream = 3 hours

We can set up the following equations based on the given information: 1. Distance = Speed × Time 2. Speed downstream = b + c 3. Speed upstream = b - c 4. Distance downstream = (b + c) × 2 5. Distance upstream = (b - c) × 3

We are also given that the boat covers the same distance in both directions.

Equating the distances: Distance downstream = Distance upstream

Substituting the distance formulas: (b + c) × 2 = (b - c) × 3

Solving for b and c will give us the speed of the boat and the speed of the current.

Calculation

Let's solve the equation: (b + c) × 2 = (b - c) × 3

Expanding and simplifying: 2b + 2c = 3b - 3c

Rearranging terms: 2c + 3c = 3b - 2b 5c = b

Now, we know that b = 5c.

Conclusion

The boat's speed is 5 times the speed of the current. This means that the boat's speed is 5 units and the current's speed is 1 unit. Therefore, the boat's speed is 5 and the current's speed is 1.

To find the time it takes for the raft to cover the same distance, we can use the formula: Time = Distance / Speed

Given that the time taken by the boat is 2 hours downstream and 3 hours upstream, the average speed of the boat is: Average speed = (2b × 3c) / (2b + 3c)

Substituting the values of b and c: Average speed = (2*5*3*1) / (2*5 + 3*1) Average speed = 30 / 13 Average speed = 2.3077

Finally, to find the time taken by the raft to cover the same distance: Time = Distance / Average speed Time = 12 / 2.3077 Time ≈ 5.2 hours

So, the time taken by the raft to cover the same distance is approximately 5.2 hours.