Question

Скорость течения реки 5км ч. Теплоход проплыл по течению 240км за 8ч. Какое время необходимо затратить ему на обратный путь,если собственная скорость теплохода не изменилась?

Answer 1

240:8=30 км/ч скорость теплохода по течению.
30-5=25 км/ч собственная скорость теплохода.
25-5=20 км/ч скорость теплохода против течения.
240:20=12 часов теплоход затратит, чтобы проплыть 240 км против течения.
Ответ: 12 часов.

Answer 2

Problem Analysis

We are given that the speed of the river current is 5 km/h and a steamboat traveled 240 km downstream in 8 hours. We need to determine how much time it will take for the steamboat to return on the upstream journey, assuming its own speed remains unchanged.

Downstream Journey

Let's first analyze the downstream journey. When the steamboat is traveling downstream, it benefits from the speed of the river current, which adds to its own speed. This allows the steamboat to cover the distance in less time compared to its own speed alone.

Upstream Journey

On the upstream journey, the steamboat has to work against the current of the river. This means that the effective speed of the steamboat will be reduced by the speed of the river current. As a result, the steamboat will take more time to cover the same distance compared to its own speed alone.

Solution

To find the time required for the steamboat to return on the upstream journey, we can use the concept of relative speed. The relative speed is the difference between the speed of the steamboat and the speed of the river current.

Let's denote the speed of the steamboat as x km/h. Since the speed of the river current is 5 km/h, the effective speed of the steamboat on the upstream journey will be (x - 5) km/h.

We know that the steamboat covered 240 km downstream in 8 hours. Using the formula distance = speed × time, we can write the equation:

240 = (x + 5) × 8 Simplifying the equation, we get:

8x + 40 = 240

Solving for x, we find:

x = 25

Therefore, the speed of the steamboat is 25 km/h.

Now, let's calculate the time required for the steamboat to return on the upstream journey. The effective speed of the steamboat on the upstream journey is (25 - 5) = 20 km/h.

Using the formula distance = speed × time, we can write the equation:

240 = 20 × time

Simplifying the equation, we find:

time = 240 / 20 = 12 hours

Therefore, it will take the steamboat 12 hours to return on the upstream journey, assuming its own speed remains unchanged.

Answer

The steamboat will need to spend 12 hours on the return journey, assuming its own speed remains unchanged.

Answer 3

Problem Analysis

We are given that the speed of the river current is 5 km/h and a steamboat traveled 240 km downstream in 8 hours. We need to determine the time it will take for the steamboat to travel back upstream if its own speed remains unchanged.

Downstream Speed Calculation

To calculate the speed of the steamboat downstream, we can subtract the speed of the river current from the speed at which the steamboat traveled downstream. Let's denote the speed of the steamboat as x km/h.

The formula to calculate the speed of the steamboat downstream is: Downstream Speed = Speed of Steamboat + Speed of River Current

Given that the speed of the river current is 5 km/h and the steamboat traveled 240 km downstream in 8 hours, we can set up the following equation: 240 km = (x + 5 km/h) * 8 hours

Upstream Speed Calculation

To calculate the speed of the steamboat upstream, we can subtract the speed of the river current from the speed at which the steamboat traveled upstream. Let's denote the speed of the steamboat upstream as y km/h.

The formula to calculate the speed of the steamboat upstream is: Upstream Speed = Speed of Steamboat - Speed of River Current

Since the speed of the steamboat remains unchanged, we can set up the following equation: x km/h = y km/h

Time Calculation for the Return Trip

To calculate the time it will take for the steamboat to travel back upstream, we can use the formula: Time = Distance / Speed

Given that the distance traveled downstream is 240 km and the speed of the steamboat upstream is y km/h, we can calculate the time as follows: Time = 240 km / y km/h

Solution

To find the time required for the steamboat to travel back upstream, we need to solve the equations we derived.

From the equation 240 km = (x + 5 km/h) * 8 hours, we can solve for x: 240 km = (x + 5 km/h) * 8 hours 240 km = 8x + 40 km/h 200 km = 8x x = 25 km/h

Since the speed of the steamboat remains unchanged, we can set y = x = 25 km/h.

Now, we can calculate the time required for the steamboat to travel back upstream: Time = 240 km / y km/h Time = 240 km / 25 km/h Time = 9.6 hours

Therefore, it will take the steamboat 9.6 hours to travel back upstream.

Answer

The steamboat will need to spend approximately 9.6 hours on the return trip if its own speed remains unchanged.