Question

Лодка прошла по течению 24 км, а затем вернулась обратно, затратив на весь путь 16 часов, какова собственная скорость лодки, если скорость течения 2 км\ч

Answer 1

Х собственная скорость лодки
х+2 скорость по течению
х-2 против течения
24/(х+2)+24/(х-2)=16
решение уравнения в приложении

Answer 2

Calculation of the Boat's Speed

To calculate the boat's speed, we need to consider the distance traveled and the time taken.

Given: - Distance traveled downstream: 24 km - Total time taken for the round trip: 16 hours - Speed of the current: 2 km/h

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

1. Downstream Journey: During the downstream journey, the boat's speed is increased by the speed of the current. Therefore, the effective speed of the boat is the sum of its own speed and the speed of the current.

Let's assume the speed of the boat is x km/h.

The time taken for the downstream journey can be calculated using the formula: Time = Distance / Speed

For the downstream journey, the distance is 24 km and the effective speed is the sum of the boat's speed and the speed of the current (x + 2 km/h).

Therefore, the time taken for the downstream journey is: Time_downstream = 24 km / (x + 2) km/h

2. Upstream Journey: During the upstream journey, the boat's speed is reduced by the speed of the current. Therefore, the effective speed of the boat is the difference between its own speed and the speed of the current.

The time taken for the upstream journey can be calculated using the same formula: Time = Distance / Speed

For the upstream journey, the distance is also 24 km, but the effective speed is the difference between the boat's speed and the speed of the current (x - 2 km/h).

Therefore, the time taken for the upstream journey is: Time_upstream = 24 km / (x - 2) km/h

3. Total Time: The total time taken for the round trip is given as 16 hours.

Since the boat traveled downstream and then returned upstream, the total time can be calculated as the sum of the time taken for the downstream journey and the time taken for the upstream journey.

Therefore, we have the equation: Time_downstream + Time_upstream = 16 hours

Now, we can solve this equation to find the value of x, which represents the boat's own speed.

Let's substitute the values into the equation and solve for x:

24 km / (x + 2) km/h + 24 km / (x - 2) km/h = 16 hours

To solve this equation, we can multiply both sides by (x + 2)(x - 2) to eliminate the denominators:

24(x - 2) + 24(x + 2) = 16(x + 2)(x - 2)

Expanding and simplifying the equation:

24x - 48 + 24x + 48 = 16(x^2 - 4)

48x = 16x^2 - 64

16x^2 - 48x - 64 = 0

Now, we can solve this quadratic equation to find the value of x.

Using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a)

where a = 16, b = -48, and c = -64.

Solving the equation, we get two possible values for x: x = 6 or x = -2/3.

Since the speed of the boat cannot be negative, we can discard the negative value.

Therefore, the boat's own speed is 6 km/h.

Please note that the solution provided is based on the given information and assumptions. If there are any additional factors or constraints that need to be considered, please provide them for a more accurate answer.