Question

Моторная лодка прошла против течения реки 112 км и вернулась в пункт отправления, затратив на обратный путь на 6 часов меньше. Найдите скорость течения , если скорость лодки в неподвижной воде равна 11 км/ч .__исходя из условия получается вот такое уравнение 112/ 11-х - 112/ 11+ х = 6 только оно у меня не решается, помогите пожалуйста

Answer 1

Решение во вложении если можно отметьте как лучший

Answer 2

Problem Analysis

We are given that a motorboat traveled 112 km against the current of a river and then returned to the starting point, spending 6 hours less on the return journey. We need to find the speed of the current, given that the speed of the boat in still water is 11 km/h.

Solution

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

When the boat is traveling against the current, its effective speed is reduced by the speed of the current. Therefore, the boat's speed against the current is (11 - x) km/h.

When the boat is traveling with the current, its effective speed is increased by the speed of the current. Therefore, the boat's speed with the current is (11 + x) km/h.

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

For the journey against the current: - Distance = 112 km - Speed = (11 - x) km/h - Time = 112 / (11 - x) hours

For the return journey with the current: - Distance = 112 km - Speed = (11 + x) km/h - Time = 112 / (11 + x - 6) hours (since the return journey took 6 hours less)

We can set up the equation: 112 / (11 - x) = 112 / (11 + x - 6) + 6

Simplifying the equation: 112 / (11 - x) = 112 / (x + 5) + 6

To solve this equation, we can cross-multiply and solve for x.

Let's solve the equation step by step:

112 / (11 - x) = 112 / (x + 5) + 6

Multiply both sides by (11 - x)(x + 5) to eliminate the denominators:

112(x + 5) = 112(11 - x) + 6(x + 5)(11 - x)

Expand and simplify:

112x + 560 = 1232 - 112x + 66(x + 5) - 6(x + 5)(x - 11)

Simplify further:

112x + 560 = 1232 - 112x + 66x + 330 - 6(x^2 - 6x - 55)

Rearrange the equation to form a quadratic equation:

6x^2 - 6x - 55 - 112x - 66x + 112x - 560 + 1232 - 330 = 0

Combine like terms:

6x^2 - 12x + 277 = 0

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

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

a = 6, b = -12, c = 277

Substituting the values into the quadratic formula:

x = (-(-12) ± √((-12)^2 - 4 * 6 * 277)) / (2 * 6)

Simplifying:

x = (12 ± √(144 - 6648)) / 12

x = (12 ± √(-6504)) / 12

Since the value inside the square root is negative, the equation does not have real solutions. This means that there is no solution for the speed of the current that satisfies the given conditions.

Therefore, based on the given information, it is not possible to determine the speed of the current.

Conclusion

Based on the given information, it is not possible to determine the speed of the current. The equation derived from the problem does not have real solutions.