Question

Задача Турист проплыл 6 км против течения реки и 15 км озером, потратив на путь озером на 1 час. больше, чем на путь по реке. Найти собственную путь скорость лодки, если скорость реки 2 км / ч.

Answer 1

Собств. скорость = х, скорость против теч. = ( х -2).
Время по реке 6 : ( х-2), по озеру 15 : х. .
15 / х - 6 / (х-2) = 1
15х - 30 - 6х = х квадрат - 2х
х1 = 5км/ч, х2 = 6 км/ч.

Answer 2

Пусть х км/ч - собственная скорость лодки.
Тогда скорость по течению (х+2) км/ч, против течения (х-2) км/ч.
Время против течения $\frac{6}{x-2}$ ч.
Время по озеру $\frac{15}{x}$ ч. 
 Составим уравнение.
$\frac{15}{x}-\frac{6}{x-2}=1; 15*(x-2)-6x=x(x-2); 15x-30-6x=x^{2}-2x;$

Answer 3

Problem Analysis

The problem states that a tourist swam 6 km against the current of a river and then swam 15 km across a lake. The time taken to swim across the lake was 1 hour more than the time taken to swim against the current of the river. The speed of the river is given as 2 km/h. We need to find the speed of the tourist's boat.

Solution

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

The time taken to swim against the current of the river is given by the formula: time = distance / speed

Therefore, the time taken to swim against the current of the river is: 6 km / (x - 2 km/h)

The time taken to swim across the lake is given by the formula: time = distance / speed

Therefore, the time taken to swim across the lake is: 15 km / x km/h

According to the problem, the time taken to swim across the lake is 1 hour more than the time taken to swim against the current of the river. So we can set up the following equation:

15 km / x km/h = 6 km / (x - 2 km/h) + 1 hour

Let's solve this equation to find the value of x.

Calculation

To solve the equation, we can start by multiplying both sides of the equation by x(x - 2) to eliminate the denominators:

15(x - 2) = 6x + x(x - 2)

Simplifying the equation:

15x - 30 = 6x + x^2 - 2x

Combining like terms:

x^2 + 7x - 30 = 0

Now we can solve this quadratic equation using factoring, completing the square, or the quadratic formula. Let's use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, a = 1, b = 7, and c = -30. Substituting these values into the quadratic formula:

x = (-7 ± √(7^2 - 4(1)(-30))) / (2(1))

Simplifying:

x = (-7 ± √(49 + 120)) / 2

x = (-7 ± √169) / 2

x = (-7 ± 13) / 2

So we have two possible solutions for x:

x1 = (-7 + 13) / 2 = 3 km/h

x2 = (-7 - 13) / 2 = -10 km/h

Since speed cannot be negative, we discard the negative solution. Therefore, the speed of the tourist's boat is 3 km/h.

Answer

The speed of the tourist's boat is 3 km/h.