Question

Лодка плыла 2 часа по течению реки и 3 часа против течения,пройдя за это время 36 км. Скорость лодки против течения реки в 3 раза меньше,чем скорость лодки по течению.Чему равна собственная скорость лодки и скорость течения реки? Умоляю,помогите мне пожалуйста!

Answer 1

Решаем систему: 2(л+р) - 3(л-р)=36, 3(л-р)=(л+р). Подставим:
2(л+р)+(л+р)=36  3(л-р)=(л+р)
Из первого л+р=12  из второго л-р=4, отсюда 2л=16, л=8, р=8-4=4.

Answer 2

Problem Analysis

We are given that a boat traveled for 2 hours with the current of a river and 3 hours against the current, covering a total distance of 36 km. The speed of the boat against the current is 3 times slower than the speed of the boat with the current. We need to find the speed of the boat in still water and the speed of the river current.

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

Solution

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

1. When the boat is traveling with the current, the effective speed is the sum of the boat's speed and the current's speed. So, the distance traveled with the current is (x + y) × 2 km. 2. When the boat is traveling against the current, the effective speed is the difference between the boat's speed and the current's speed. So, the distance traveled against the current is (x - y) × 3 km.

According to the problem, the sum of these two distances is equal to 36 km:

(x + y) × 2 + (x - y) × 3 = 36

Simplifying the equation:

2x + 2y + 3x - 3y = 36

5x - y = 36

We also know that the speed of the boat against the current is 3 times slower than the speed of the boat with the current:

x - y = 3(x + y)

Simplifying the equation:

x - y = 3x + 3y

-2x - 4y = 0

Now we have a system of two equations:

5x - y = 36

-2x - 4y = 0

We can solve this system of equations to find the values of x and y.

Solution Steps

1. Solve the system of equations: - Multiply the second equation by 2 to eliminate the coefficient of x: -4x - 8y = 0 - Add the two equations: 5x - y + (-4x - 8y) = 36 + 0 - Simplify: x - 9y = 36 - Rearrange the equation: x = 36 + 9y 2. Substitute the value of x in terms of y into the first equation: 5(36 + 9y) - y = 36 3. Solve for y: - Simplify the equation: 180 + 45y - y = 36 - Combine like terms: 44y = -144 - Divide both sides by 44: y = -3.27 4. Substitute the value of y back into the equation for x: x = 36 + 9(-3.27) 5. Solve for x: - Simplify the equation: x = 36 - 29.43 - Calculate: x = 6.57

Answer

The speed of the boat in still water is approximately 6.57 km/h and the speed of the river current is approximately -3.27 km/h. The negative sign indicates that the current is flowing in the opposite direction of the boat's motion.

Please note that the negative value for the speed of the river current may not make physical sense in this context. It is possible that there was an error in the problem statement or in the calculations.