Question

ЗАДАЧА! Катер проплыв по течению 16 км и против течения 12 км, на весь путь, затратил 5 часов Найдите собственную скорость катера, если скорость течения реки 2 км/ч

Answer 1

1)16-2=14(км/ч)скорость катера
14 км/ч скорость катера.

Answer 2

Problem Analysis

We are given that a boat travels 16 km downstream and 12 km upstream, taking a total of 5 hours. The speed of the river current is given as 2 km/h. 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 downstream, 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, 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 given by the equation: 16 km = (x + 2) km/h × t1 hours The time taken to travel upstream is given by the equation: 12 km = (x - 2) km/h × t2 hours We are also given that the total time taken for the entire journey is 5 hours: t1 + t2 = 5 hours We can solve this system of equations to find the value of x, the speed of the boat in still water.

Solution Steps

1. Rearrange equation to solve for t1: t1 = 16 km / (x + 2) km/h 2. Rearrange equation to solve for t2: t2 = 12 km / (x - 2) km/h 3. Substitute equations and into equation 16 km / (x + 2) km/h + 12 km / (x - 2) km/h = 5 hours 4. Multiply both sides of equation by (x + 2)(x - 2) to eliminate the denominators: 16(x - 2) + 12(x + 2) = 5(x + 2)(x - 2) 5. Expand and simplify equation 16x - 32 + 12x + 24 = 5(x^2 - 4)

Simplifying further: 28x - 8 = 5x^2 - 20

Rearranging the equation: 5x^2 - 28x + 12 = 0 6. Solve equation for x using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a)

Substituting the values of a, b, and c: x = (-(-28) ± √((-28)^2 - 4(5)(12))) / (2(5))

Simplifying further: x = (28 ± √(784 - 240)) / 10

x = (28 ± √544) / 10

x = (28 ± 23.32) / 10

Therefore, the possible values for x are: x = (28 + 23.32) / 10 or x = (28 - 23.32) / 10

x = 5.832 or x = 0.168

Since the speed of the boat cannot be negative, the speed of the boat in still water is 5.832 km/h.

Answer

The speed of the boat in still water is 5.832 km/h.