Question

Теплоход, собственная скорость которого 16 км\ч прошёл 50 км по течению реки и 8 км против течения, затратив на весь путь 3 часа. Какова скорость течения реки, если известно, что она не превосходит 10 км\ч ? (возможные ответы: а) 2 км\ч б) 8 км\ч в) 3 км\ч г) 5 км\ч. ) помогите пожалуйста!!! заранее: БОЛЬШОЕ СПАСИБО!!!

Answer 1

Ответ Б, 8 км/ч
решить можно с помощью данного уравнения: 50/16+х + 8/16-х = 3

Answer 2

Problem Analysis

We are given that a boat with a speed of 16 km/h traveled 50 km downstream and 8 km upstream, taking a total of 3 hours for the entire journey. We need to determine the speed of the river's current, knowing that it does not exceed 10 km/h.

Solution

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

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

1. Downstream journey: - The boat's speed relative to the ground is the sum of its own speed and the speed of the river's current: (16 + x) km/h. - The distance traveled downstream is 50 km. - The time taken for the downstream journey is 50 / (16 + x) hours.

2. Upstream journey: - The boat's speed relative to the ground is the difference between its own speed and the speed of the river's current: (16 - x) km/h. - The distance traveled upstream is 8 km. - The time taken for the upstream journey is 8 / (16 - x) hours.

3. Total time: - The total time for the entire journey is given as 3 hours.

Using the information above, we can set up the following equation:

50 / (16 + x) + 8 / (16 - x) = 3

Now, let's solve this equation to find the value of x.

Calculation

To solve the equation, we can multiply both sides by the denominators to eliminate the fractions:

50(16 - x) + 8(16 + x) = 3(16 + x)(16 - x)

Simplifying the equation:

800 - 50x + 128 + 8x = 768 - 3x^2

Combining like terms:

928 - 42x = 768 - 3x^2

Rearranging the equation:

3x^2 - 42x + 160 = 0

Now, we can solve this quadratic equation using the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, a = 3, b = -42, and c = 160.

Plugging in the values:

x = (-(-42) ± √((-42)^2 - 4 * 3 * 160)) / (2 * 3)

Simplifying:

x = (42 ± √(1764 - 1920)) / 6

x = (42 ± √(-156)) / 6

Since the square root of a negative number is not a real number, it means that there is no real solution for the equation. This implies that there is no valid speed of the river's current that satisfies the given conditions.

Therefore, the answer is there is no valid speed of the river's current.

Answer

The speed of the river's current cannot be determined based on the given information.