Question

Лодка спускается по течению реки на расстояние 10 км, а затем поднимается против течения на расстояние 6 км. Скорость течения реки равна 1 км/ч. В каких пределах должна быть собственная скорость лодки, чтобы вся поездка заняла от 3 до 4 часов.

Answer 1

Вот полное решение http://festival.1september.ru/articles/100981/img9.gif

Answer 2

Problem Analysis

We are given the following information: - The boat travels downstream for a distance of 10 km. - The boat then travels upstream for a distance of 6 km. - The speed of the river current is 1 km/h. - The total duration of the trip should be between 3 and 4 hours.

We need to determine the range of the boat's speed in order for the entire trip to take between 3 and 4 hours.

Solution

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

Let's break down the problem into two parts: the downstream journey and the upstream journey.

# Downstream Journey

During the downstream journey, the boat's speed is the sum of its own speed and the speed of the river current. Let's denote the boat's speed as x km/h.

The time taken for the downstream journey can be calculated as: time_downstream = distance_downstream / (boat_speed + river_current_speed)

Substituting the given values: time_downstream = 10 / (x + 1)

# Upstream Journey

During the upstream journey, the boat's speed is the difference between its own speed and the speed of the river current. Let's denote the boat's speed as x km/h.

The time taken for the upstream journey can be calculated as: time_upstream = distance_upstream / (boat_speed - river_current_speed)

Substituting the given values: time_upstream = 6 / (x - 1)

# Total Time

The total time for the trip is the sum of the downstream and upstream times: total_time = time_downstream + time_upstream

Substituting the previously calculated values: total_time = 10 / (x + 1) + 6 / (x - 1)

We need to find the range of values for x that will make the total time fall between 3 and 4 hours.

Calculation

Let's calculate the range of values for x that will make the total time fall between 3 and 4 hours.

Using the formula total_time = 10 / (x + 1) + 6 / (x - 1), we can substitute the values of x and calculate the total time for different values.

For x = 2: total_time = 10 / (2 + 1) + 6 / (2 - 1) = 10 / 3 + 6 = 10/3 + 18/3 = 28/3 ≈ 9.33 hours

For x = 3: total_time = 10 / (3 + 1) + 6 / (3 - 1) = 10 / 4 + 6 / 2 = 5/2 + 3 = 5/2 + 6/2 = 11/2 = 5.5 hours

For x = 4: total_time = 10 / (4 + 1) + 6 / (4 - 1) = 10 / 5 + 6 / 3 = 2 + 2 = 4 hours

For x = 5: total_time = 10 / (5 + 1) + 6 / (5 - 1) = 10 / 6 + 6 / 4 = 5/3 + 3/2 = 10/6 + 9/6 = 19/6 ≈ 3.17 hours

From the calculations, we can see that the total time falls between 3 and 4 hours when the boat's speed (x) is between 4 km/h and 5 km/h.

Answer

The boat's speed should be between 4 km/h and 5 km/h in order for the entire trip to take between 3 and 4 hours.