Question

Найдите скорость лодки в неподвижной воде, если скорость течения равна 3 км/ч. Лодка прошла по течению реки 36 км и вернулась обратно, потратив на весь путь 5 часов.

Answer 1

Скорость лодки х
скорость по теч. х+3
скорость против теч. х-3
время движения по теч 36/(х+3)
время движения против теч 36/(х-3)
т.к. на весь путь ушло 5 часов, то
36/(х+3)+36/(х-3)=5

Answer 2

Calculation of Boat Speed in Still Water

To find the speed of the boat in still water, we can use the concept of relative velocity. The speed of the boat in still water can be calculated by subtracting the speed of the current from the total speed of the boat in both directions.

Let's denote the speed of the boat in still water as x km/h and the speed of the current as 3 km/h.

The boat traveled a total distance of 36 km along the current and back, and it took 5 hours for the entire journey.

To calculate the boat's speed in still water, we can set up the following equation:

36 / (x + 3) + 36 / (x - 3) = 5

Simplifying the equation, we get:

36(x - 3) + 36(x + 3) = 5(x + 3)(x - 3)

Solving this equation will give us the speed of the boat in still water.

Let's solve the equation step by step:

1. Expand the equation: 36x - 108 + 36x + 108 = 5(x^2 - 9)

2. Combine like terms: 72x = 5x^2 - 45

3. Rearrange the equation to form a quadratic equation: 5x^2 - 72x - 45 = 0

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

Using the quadratic formula, which states that for an equation of the form ax^2 + bx + c = 0, the solutions for x are given by:

x = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, a = 5, b = -72, and c = -45.

Plugging in these values, we get:

x = (-(-72) ± √((-72)^2 - 4 * 5 * (-45))) / (2 * 5)

Simplifying further:

x = (72 ± √(5184 + 900)) / 10

x = (72 ± √(6084)) / 10

x = (72 ± 78) / 10

So, we have two possible solutions for x:

1. x = (72 + 78) / 10 = 15 km/h 2. x = (72 - 78) / 10 = -0.6 km/h

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

Therefore, the speed of the boat in still water is 15 km/h.

Answer:

The speed of the boat in still water is 15 km/h.