Question

Катер прошёл 10 км против течения ,а затем 45 по течению, затратив на весь путь 2 часа . найдите собственную скорость катера ,если скорость течения реки 5 км/час

Answer 1

2часа это= 120 мин 
5км это=5000
10км это=10000
 45:2=25

Answer 2

Problem Analysis

We are given that a boat traveled 10 km against the current and then 45 km with the current. The total time taken for the entire journey was 2 hours. We need to find the speed of the boat in still water.

Solution

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

When the boat is traveling against the current, its effective speed is reduced by the speed of the current. So, the speed of the boat against the current is (x - 5) km/h.

When the boat is traveling with the current, its effective speed is increased by the speed of the current. So, the speed of the boat with the current is (x + 5) 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 10 km against the current is 10 / (x - 5) hours.

The time taken to travel 45 km with the current is 45 / (x + 5) hours.

According to the problem, the total time taken for the entire journey is 2 hours. So, we can write the equation:

10 / (x - 5) + 45 / (x + 5) = 2

To solve this equation, we can multiply both sides by (x - 5)(x + 5) to eliminate the denominators.

10(x + 5) + 45(x - 5) = 2(x - 5)(x + 5)

Simplifying the equation:

10x + 50 + 45x - 225 = 2(x^2 - 25)

55x - 175 = 2x^2 - 50

Rearranging the equation:

2x^2 - 55x + 125 = 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), where a = 2, b = -55, and c = 125.

Substituting the values into the formula:

x = (-(-55) ± √((-55)^2 - 4 * 2 * 125)) / (2 * 2)

Simplifying:

x = (55 ± √(3025 - 1000)) / 4

x = (55 ± √2025) / 4

x = (55 ± 45) / 4

We have two possible solutions:

1. x = (55 + 45) / 4 = 100 / 4 = 25 2. x = (55 - 45) / 4 = 10 / 4 = 2.5

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

Therefore, the speed of the boat in still water is 25 km/h.

Answer

The speed of the boat in still water is 25 km/h.