Question

Катер прошел по течению 5 часов, а против за 6 часов сколько времени будет в пути плот?

Answer 1

Весь путь примем за единицу (целое)
1/5 (км/ч) - скорость катера по течению реки
1/6 (км/ч) - скорость катера против течения реки
-------------------------------------------------
1) (1/5 - 1/6) : 2 = (6/30 - 5/30) : 2 = 1/30 : 2 = 1/30 * 1/2 = 1/60 (км/ч) - скорость течения реки;
2) 1 : 1/60 = 1 * 60/1 = 60 (ч) - столько времени будет в пути плот.
Ответ: 60 часов. 

Answer 2

Calculation of Time for the Journey

To calculate the time it will take for the raft to travel, we need to consider the time it takes for the boat to travel with the current and against the current.

Let's assume that the speed of the boat in still water is x units per hour, and the speed of the current is y units per hour.

When the boat is traveling with the current, its effective speed is the sum of the speed of the boat and the speed of the current. So, the boat will cover a distance of (x + y) units in 5 hours.

When the boat is traveling against the current, its effective speed is the difference between the speed of the boat and the speed of the current. So, the boat will cover a distance of (x - y) units in 6 hours.

To find the speed of the boat in still water, we can use the formula:

Speed of the boat in still water = (Distance traveled with the current - Distance traveled against the current) / (Time taken with the current + Time taken against the current)

Substituting the values we have:

Speed of the boat in still water = ((x + y) * 5 - (x - y) * 6) / (5 + 6)

Simplifying the equation:

Speed of the boat in still water = (5x + 5y - 6x + 6y) / 11

Speed of the boat in still water = (y - x) / 11

Now, we can calculate the time it will take for the raft to travel a certain distance.

Let's assume the distance is d units.

When the boat is traveling with the current, the time taken is given by:

Time taken with the current = d / (x + y)

When the boat is traveling against the current, the time taken is given by:

Time taken against the current = d / (x - y)

Adding the two times together, we get the total time taken for the journey:

Total time taken = d / (x + y) + d / (x - y)

Simplifying the equation:

Total time taken = (2dx) / (x^2 - y^2)

Therefore, the total time taken for the raft to travel a certain distance is (2dx) / (x^2 - y^2).

Please note that the above calculations assume a constant speed of the boat and current throughout the journey, which may not always be the case in real-world scenarios.