Question

Катер прошол 15км по течению реки и 4 км по озеру, затратив на весь путь 1 час.Найдите скорость катера по течению реки,если скорость течения реки равна 4км/ч

Answer 1

1)15+4=19(км) весь путь
2)19км:1ч=19(км/ч) скорость катера
3)19+4=23(км/ч)скорость по течению
4)19-4=15(км/ч)скорость против течения
Ответ: 15 км/ч и 23 км/ч.

Answer 2

Problem Analysis

We are given that a boat traveled 15 km downstream in a river and 4 km on a lake, taking a total of 1 hour for the entire journey. We need to find the speed of the boat downstream in the river, given that the speed of the river's current is 4 km/h.

Solution

Let's assume the speed of the boat downstream in the river is x km/h.

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

The time taken to travel downstream in the river is given by: time1 = 15 km / (x + 4 km/h).

The time taken to travel on the lake is given by: time2 = 4 km / x km/h.

Since the total time taken for the entire journey is 1 hour, we can write the equation: time1 + time2 = 1 hour.

Substituting the values of time1 and time2, we get: 15 / (x + 4) + 4 / x = 1.

To solve this equation, we can multiply through by x(x + 4) to eliminate the denominators.

Simplifying the equation, we get: 15x + 60 + 4(x + 4) = x(x + 4).

Expanding and rearranging the equation, we get: x^2 - 7x - 76 = 0.

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

Quadratic Equation Solution

Using the quadratic formula, we can find the values of x that satisfy the equation x^2 - 7x - 76 = 0.

The quadratic formula is given by: x = (-b ± √(b^2 - 4ac)) / (2a).

For our equation, a = 1, b = -7, and c = -76.

Substituting these values into the quadratic formula, we get: x = (7 ± √(49 + 304)) / 2.

Simplifying further, we get: x = (7 ± √(353)) / 2.

Calculating the square root of 353, we get: √(353) ≈ 18.79.

Substituting this value into the equation, we get: x ≈ (7 ± 18.79) / 2.

Simplifying further, we get two possible values for x: x ≈ 12.89 or x ≈ -5.89.

Since the speed of the boat cannot be negative, we can discard the value of x ≈ -5.89.

Therefore, the speed of the boat downstream in the river is approximately 12.89 km/h.

Answer

The speed of the boat downstream in the river is approximately 12.89 km/h.