Question

Турист проплылна байдарке 15км против течения реки и 14км по её течению. затратив на все путешесвие столько же времени, сколько ему понадобилось бы, чтобы проплыть в стоячей воде 30км. Найти собственную скорость байдарки, если скорость течения реки 1км/ч.решение с помощью квадратного уравнения!!!Решите пожалуйста оченьнадо!

Answer 1

30/x=15/(x-1)+14/(x+1)=(29x+1)/(x^2-1)

x^2-x-30=0

x=(1+11)/2=6

ответ скорость лодки 6 км в час

Answer 2

Problem Analysis

We are given that a tourist paddled a kayak for 15 km against the current of a river and then paddled 14 km with the current. The time taken for this journey is the same as the time it would take to paddle 30 km in still water. We need to find the speed of the kayak.

Let's assume the speed of the kayak in still water is x km/h. The speed of the river's current is given as 1 km/h.

Solution

To solve this problem, we can use the formula: time = distance / speed.

The time taken to paddle against the current for 15 km is given by: time1 = 15 / (x - 1).

The time taken to paddle with the current for 14 km is given by: time2 = 14 / (x + 1).

The time taken to paddle in still water for 30 km is given by: time3 = 30 / x.

According to the problem, time1 + time2 = time3.

Substituting the values, we get: 15 / (x - 1) + 14 / (x + 1) = 30 / x.

To solve this equation, we can multiply through by x(x - 1)(x + 1) to eliminate the denominators.

Simplifying the equation, we get: 15x(x + 1) + 14x(x - 1) = 30(x - 1)(x + 1).

Expanding and simplifying further, we get a quadratic equation: 29x^2 - 16x - 30 = 0.

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

Solving the Quadratic Equation

To solve the quadratic equation 29x^2 - 16x - 30 = 0, we can use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a).

In this case, a = 29, b = -16, and c = -30.

Substituting the values into the quadratic formula, we get: x = (-(-16) ± √((-16)^2 - 4 * 29 * (-30))) / (2 * 29).

Simplifying further, we get: x = (16 ± √(256 + 3480)) / 58.

Calculating the values inside the square root, we get: x = (16 ± √(3736)) / 58.

Taking the square root of 3736, we get: √(3736) ≈ 61.09.

Substituting this value into the equation, we get: x = (16 ± 61.09) / 58.

Calculating the two possible values of x, we get: x ≈ 1.84 or x ≈ -0.69.

Since the speed of the kayak cannot be negative, we can discard the negative value.

Therefore, the speed of the kayak in still water is approximately 1.84 km/h.

Answer

The speed of the kayak in still water is approximately 1.84 km/h.