Question

Катер проплыл 40 км за течением речки и 16 км против течения,использовав на весь путь 3 часа.Какая собственная скорость катера,если скорость течения 2 км/час?

Answer 1

40/(х+2)+16/(х-2)=3

40х-80+16х+32=3х²-12

3х²-56х+36=0

D/4=784-108=676    √D=26

x=(28±26)/3=2/3;18.     2/3 - посторонний корень

Ответ: 18.

Answer 2

Время по течению 40/(v+2), время против течения 16/(v-2). Если сложить эти времена, получим 3 часа.

 

40/(v+2)+16/(v-2)=3

40(v-2)+16(v+2)=3(v^2-4)

56v-48=3v^2-12

3v^2-56v+36=0

Решив квадратное уравнение, получим v=18 км/ч

 

Answer 3

Problem Analysis

We are given the following information: - The boat traveled 40 km downstream (with the current) and 16 km upstream (against the current). - The total time taken for the entire journey was 3 hours. - The speed of the current is 2 km/h.

We need to find the speed of the boat.

Solution

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

When the boat is traveling downstream (with the current), its effective speed is the sum of its own speed and the speed of the current. Therefore, the boat's effective speed downstream is (x + 2) km/h.

When the boat is traveling upstream (against the current), its effective speed is the difference between its own speed and the speed of the current. Therefore, the boat's effective speed upstream is (x - 2) km/h.

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

The time taken to travel downstream is 40 km / (x + 2) km/h.

The time taken to travel upstream is 16 km / (x - 2) km/h.

According to the problem, the total time taken for the entire journey is 3 hours. Therefore, we can write the equation:

(40 / (x + 2)) + (16 / (x - 2)) = 3

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

40(x - 2) + 16(x + 2) = 3(x + 2)(x - 2)

Simplifying the equation will give us a quadratic equation, which we can solve to find the value of x.

Let's solve the equation step by step:

1. Expand the equation: 40x - 80 + 16x + 32 = 3(x^2 - 4) Simplifying further: 56x - 48 = 3x^2 - 12

2. Rearrange the equation to form a quadratic equation: 3x^2 - 56x + 12 - 48 = 0 Simplifying further: 3x^2 - 56x - 36 = 0

3. Solve the quadratic equation using the quadratic formula: The quadratic formula is given by: x = (-b ± √(b^2 - 4ac)) / (2a) For our equation, a = 3, b = -56, and c = -36.

Plugging in the values, we get: x = (-(-56) ± √((-56)^2 - 4 * 3 * -36)) / (2 * 3) Simplifying further: x = (56 ± √(3136 + 432)) / 6 x = (56 ± √(3568)) / 6 x = (56 ± 59.7) / 6

Therefore, we have two possible solutions: - x = (56 + 59.7) / 6 ≈ 18.95 km/h - x = (56 - 59.7) / 6 ≈ -0.95 km/h

Since the speed of the boat cannot be negative, we can discard the negative solution.

4. Therefore, the speed of the boat is approximately 18.95 km/h.

Answer

The speed of the boat is approximately 18.95 km/h.