Question

Катер прошел против течения реки 21 км и по течению 8 км, затратив на весь путь 2 часа. Найдите скорость катера в стоячей воде, если скорость течения реки 1 км/ч. Помогите пожалуйста очень надо)

Answer 1

Пусть х-скорость катера в стоячей воде,

тогда скорость катера по течению равна х+1 км/ч,

а скорость катера против течения равна х-1 км/ч.

На путь по течению катер затратил 8/(х+1) часа,

а на путь против течения 21/(х-1) часа.

По условию на весь путь затрачено 2 часа.

Составим уравнение:

8/(х+1) + 21/(х-1) =2|*(x+1)(x-1)
8(x-1)+21(x+1)=2(x^2-1)

8x-8+21x+21=2x^2-2

29x+13-2x^2+2=0|*(-1)

2x^2-29x-15=0
 D=961 

х1=-0,5(км/ч)
х2= 15(км/ч) -скорость катера

Answer 2

Problem Analysis

We are given that a boat traveled 21 km against the current of a river and then traveled 8 km with the current. The total time taken for the entire journey was 2 hours. We need to find the speed of the boat in still water, given that the speed of the river current is 1 km/h.

Solution

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

When the boat is traveling against the current, its effective speed is reduced by the speed of the current. So, the boat's speed against the current is (x - 1) km/h.

When the boat is traveling with the current, its effective speed is increased by the speed of the current. So, the boat's speed with the current is (x + 1) km/h.

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

For the journey against the current: - Distance = 21 km - Speed = (x - 1) km/h - Time = Distance / Speed = 21 / (x - 1) hours

For the journey with the current: - Distance = 8 km - Speed = (x + 1) km/h - Time = Distance / Speed = 8 / (x + 1) hours

The total time for the entire journey is given as 2 hours. So, we can write the equation:

21 / (x - 1) + 8 / (x + 1) = 2

To solve this equation, we can multiply both sides by (x - 1)(x + 1) to eliminate the denominators:

21(x + 1) + 8(x - 1) = 2(x - 1)(x + 1)

Simplifying the equation:

21x + 21 + 8x - 8 = 2(x^2 - 1)

Combining like terms:

29x + 13 = 2x^2 - 2

Rearranging the equation:

2x^2 - 29x - 15 = 0

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

Calculation

Using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a), where a = 2, b = -29, and c = -15.

Substituting the values into the formula:

x = (-(-29) ± √((-29)^2 - 4 * 2 * -15)) / (2 * 2)

Simplifying:

x = (29 ± √(841 + 120)) / 4

x = (29 ± √961) / 4

x = (29 ± 31) / 4

We have two possible solutions:

1. x = (29 + 31) / 4 = 60 / 4 = 15 km/h 2. x = (29 - 31) / 4 = -2 / 4 = -0.5 km/h

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

Answer

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