Question

)моторная лодка прошла 5 км по течению реки и 6 против течения, затратив на весь путь 1,5 часа. найдите скорость течения реки, если собственная скорость лодки равна 8 км в час

Answer 1

пусть скорость течени х, тогда скорость по течению 8+х,  против течения 8-х;

время по течению  5/(8+x),   время против течения  6/(8-x).  уравнение

5/(8+x)  +  6/(8-x) = 1,5;   40-5x+48+6x=96 - 1,5x^2,  1,5x^2+x-8=0

x=-8/3 - не подходит по смыслу задачи

x=2.  Ответ: 2 км/ч скорость течения реки

Answer 2

Problem Analysis

We are given the following information: - The motorboat traveled 5 km downstream (with the current) and 6 km upstream (against the current). - The total time taken for the entire journey was 1.5 hours. - The speed of the motorboat is 8 km/h.

We need to find the speed of the river current.

Solution

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

To find the speed of the river current, we can use the formula: speed = distance / time.

# Downstream Journey:

- Distance: 5 km - Speed of the motorboat: 8 km/h - Speed of the river current: x km/h

The effective speed of the motorboat during the downstream journey is the sum of its own speed and the speed of the river current. Therefore, the effective speed is (8 + x) km/h.

The time taken for the downstream journey can be calculated using the formula: time = distance / speed.

Substituting the values, we get: time = 5 / (8 + x) hours.

# Upstream Journey:

- Distance: 6 km - Speed of the motorboat: 8 km/h - Speed of the river current: x km/h

The effective speed of the motorboat during the upstream journey is the difference between its own speed and the speed of the river current. Therefore, the effective speed is (8 - x) km/h.

The time taken for the upstream journey can be calculated using the formula: time = distance / speed.

Substituting the values, we get: time = 6 / (8 - x) hours.

# Total Time:

The total time taken for the entire journey is given as 1.5 hours. Therefore, the sum of the time taken for the downstream journey and the time taken for the upstream journey should be equal to 1.5 hours.

Mathematically, we can represent this as: (5 / (8 + x)) + (6 / (8 - x)) = 1.5.

Now, we can solve this equation to find the value of x, which represents the speed of the river current.

Calculation

Let's solve the equation (5 / (8 + x)) + (6 / (8 - x)) = 1.5 to find the value of x.

Using algebraic manipulation, we can simplify the equation as follows:

(5 / (8 + x)) + (6 / (8 - x)) = 1.5
(5(8 - x) + 6(8 + x)) / ((8 + x)(8 - x)) = 1.5
(40 - 5x + 48 + 6x) / (64 - x^2) = 1.5
(88 + x) / (64 - x^2) = 1.5
88 + x = 1.5(64 - x^2)
88 + x = 96 - 1.5x^2
1.5x^2 + x - 8 = 0

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

Using the quadratic formula, we have:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 1.5, b = 1, and c = -8.

x = (-1 ± √(1^2 - 4(1.5)(-8))) / (2(1.5))
x = (-1 ± √(1 + 48)) / 3
x = (-1 ± √49) / 3

Taking the positive value of x, we have:

x = (-1 + √49) / 3
x = (-1 + 7) / 3
x = 6 / 3
x = 2

Therefore, the speed of the river current is 2 km/h.

Answer

The speed of the river current is 2 km/h.