Question

Спортивная лодка прошла расстояние 45 км против течения реки и такое же расстояние по течению ,затратив на весь путь 14часов .Определите собственную скорость лодки ,если скорость течения реки 2км/ч.

Answer 1

$\frac{45}{x-2}+ \frac{45}{x+2}=14|*(x-2)(x+2)\\ 45(x+2)+45(x-2)=14(x-2)(x+2)\\ 45x+90+45x-90=14(x^2-4)\\ 90x=14x^2-56\\ -14x^2+90x+56=0|*(-1)\\ 14x^2-90x-56=0|:2\\ 7x^2-45x-28=0\\ D=b^2-4ac=(-45)^2-4*7*(-28)=2025-(-784)=2809\\ x_1= \frac{-b+ \sqrt{D} }{2a} = \frac{45+53}{14}= \frac{98}{14}= 7$

Второй икс находить не имеет смысла, поскольку он будет отрицательный, а скорость лодки не может быть отрицательной. 

Ответ: 7 км/ч.

Answer 2

Problem Analysis

We are given that a sports boat traveled a distance of 45 km against the current of a river and the same distance with the current, taking a total of 14 hours for the entire journey. We need to determine the speed of the boat if the speed of the river's current is 2 km/h.

Solution

Let's assume the speed of the boat is x km/h. Since the boat is traveling against the current, its effective speed will be (x - 2) km/h. Similarly, when the boat is traveling with the current, its effective speed will be (x + 2) km/h.

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

1. Against the current: - Distance: 45 km - Speed: (x - 2) km/h - Time: 45 / (x - 2) hours

2. With the current: - Distance: 45 km - Speed: (x + 2) km/h - Time: 45 / (x + 2) hours

According to the problem, the total time taken for the entire journey is 14 hours. So, we can set up the following equation:

45 / (x - 2) + 45 / (x + 2) = 14

To solve this equation, we can multiply both sides by (x - 2)(x + 2) to eliminate the denominators:

45(x + 2) + 45(x - 2) = 14(x - 2)(x + 2)

Simplifying the equation:

45x + 90 + 45x - 90 = 14(x^2 - 4)

90x = 14x^2 - 56

14x^2 - 90x - 56 = 0

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

Quadratic Equation Solution

Using the quadratic formula x = (-b ± √(b^2 - 4ac)) / (2a),#### Calculating the Boat's Speed

To determine the speed of the boat, we can use the formula: speed = distance / time

Given: - Distance traveled against the current = 45 km - Distance traveled with the current = 45 km - Total time taken = 14 hours - Speed of the river's current = 2 km/h

Let's calculate the boat's speed.

Calculations

The boat's speed can be calculated using the formula: speed = distance / time

The boat's speed against the current can be represented as (boat_speed - current_speed), and with the current as (boat_speed + current_speed).

Using the given information, we can set up the following equations: 1. 45 / (boat_speed - 2) + 45 / (boat_speed + 2) = 14

Solving this equation will give us the speed of the boat.

Solution

After solving the equation 45 / (boat_speed - 2) + 45 / (boat_speed + 2) = 14, we find that the speed of the boat is approximately 7 km/h.

Therefore, the speed of the boat is 7 km/h.