Question

Катер прошёл по течению реки 5 км, а против течения 4 км. Найти скорость катера, если скорость течения реки 3 км/ч. (решить дробью)

Answer 1

Пусть скорость катера будет x тогда скорость за течением x+3 а против течения x-3 тогда время за течением 5/x+3 а против 4/x-3 Составляю уравнение
5/x+3 + 4/x-3 = 1
X не может быть (0;3;-3)
5x-15+4x+12 - x ^(2)-3x+3x+9=0
-x^(2)+9x+6=0/(-1)
x^(2)-9x-6=0
Ответ x = 9×√(24)

Answer 2

Время которое прошел катер туда и обратно известно?

Answer 3

Problem Analysis

We are given that a boat traveled downstream for 5 km and upstream for 4 km in a river with a current speed of 3 km/h. We need to find the speed of the boat.

Solution

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

When the boat is traveling downstream, its effective speed is the sum of its speed in still water and the speed of the current. So, the effective speed downstream is (x + 3) km/h.

When the boat is traveling upstream, its effective speed is the difference between its speed in still water and the speed of the current. So, 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.

For the downstream journey, the time taken is 5 km / (x + 3) km/h.

For the upstream journey, the time taken is 4 km / (x - 3) km/h.

Since the total time taken for the round trip is the sum of the times taken for the downstream and upstream journeys, we can set up the equation:

5 / (x + 3) + 4 / (x - 3) = total time

Now, let's solve this equation to find the value of x.

Calculation

To solve the equation, we need to find a common denominator and simplify the equation. Let's multiply both sides of the equation by (x + 3)(x - 3) to eliminate the denominators:

5(x - 3) + 4(x + 3) = total time * (x + 3)(x - 3)

Simplifying the equation:

5x - 15 + 4x + 12 = total time * (x^2 - 9)

9x - 3 = total time * (x^2 - 9)

Expanding the right side of the equation:

9x - 3 = total time * x^2 - 9 * total time

Rearranging the equation:

total time * x^2 - 9 * total time - 9x + 3 = 0

This is a quadratic equation in terms of x. We can solve it using the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = total time, b = -9, and c = 3.

Let's substitute these values into the quadratic formula and solve for x.

Solution

The speed of the boat is given by the positive root of the quadratic equation:

x = (-(-9) ± √((-9)^2 - 4 * total time * 3)) / (2 * total time)

Substituting the value of total time as (5 / (x + 3) + 4 / (x - 3)):

x = (-(-9) ± √((-9)^2 - 4 * (5 / (x + 3) + 4 / (x - 3)) * 3)) / (2 * (5 / (x + 3) + 4 / (x - 3)))

Simplifying the equation further:

x = (9 ± √(81 - 12 * (5 / (x + 3) + 4 / (x - 3)))) / (10 / (x + 3) + 8 / (x - 3))

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