Question

Катер проплыл 24 км за течеей и вернулся назад, потративши на всю дорогу 4 часа 16 минут. Найдите собственную скорость катера, если скорость течии реки 3км/час​

Answer 1

Ответ:

90 км/ч

Пошаговое объяснение:

24 км = 24000 метров

4 часа 16 минут = 256 минут

24000 м : 256 мин - 3 км = 90 км/ч

Answer 2

Problem Analysis

We are given that a boat traveled 24 km downstream and then returned back, spending a total of 4 hours and 16 minutes on the entire journey. The speed of the river current is given as 3 km/h. We need to find the speed of the boat.

Solution

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

When the boat is traveling downstream, it gets a boost from the river current. So the effective speed of the boat is the sum of its own speed and the speed of the river current. Therefore, the effective speed downstream is (x + 3) km/h.

When the boat is traveling upstream, it has to overcome the resistance of the river current. So the effective speed of the boat is the difference between its own speed and the speed of the river current. Therefore, the effective speed upstream is (x - 3) km/h.

We can use the formula distance = speed × time to calculate the time taken for each leg of the journey.

1. Downstream journey: - Distance = 24 km - Speed = (x + 3) km/h - Time = Distance / Speed = 24 / (x + 3) hours

2. Upstream journey: - Distance = 24 km - Speed = (x - 3) km/h - Time = Distance / Speed = 24 / (x - 3) hours

The total time for the entire journey is given as 4 hours and 16 minutes, which is equivalent to 4 + 16/60 = 4.27 hours.

We can now set up the equation: Time downstream + Time upstream = Total time 24 / (x + 3) + 24 / (x - 3) = 4.27

To solve this equation, we can multiply both sides by (x + 3)(x - 3) to eliminate the denominators: 24(x - 3) + 24(x + 3) = 4.27(x + 3)(x - 3)

Simplifying the equation: 24x - 72 + 24x + 72 = 4.27(x^2 - 9) 48x = 4.27x^2 - 38.43

Rearranging the equation: 4.27x^2 - 48x - 38.43 = 0

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

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

For our equation: a = 4.27, b = -48, c = -38.43

Solving the equation, we get two possible values for x: x1 and x2.

Let's calculate the values of x1 and x2 using the quadratic formula.