Question

Катер шел 2 часа против течения и 3 часа по течению. За это время он прошел 88 км. Найдите скорость течения и скорость катера в стоячей воде,если по течению он прошел на 32 км больше,чем против течения. ЗАДАЧУ РЕШАТЬ С ПОМОЩЬЮ СИСТЕМЫ

Answer 1

Пусть Х-км прошел катер против течения. 
тогда (Х+32)км по течению. 
Всего прошёл 88км. 
Х+(Х+32)=88 
2Х=88-32=56 
Х=56/2=28(км) прошел катер против течения. 
Время против течения 2 часа. 
28/2=14(км/ч) скорость катера против течения 
28+32=60(км) прошел катер по течению. 
Время по течению 3 часа. 
60/3=20(км/ч )скорость катера по течению. 
Находим среднюю скорость катера. 
14+20=17(км/ч)средн.скорость катера. 
20-17=3 или 17-14=3(км/ч) скорость течения реки

Answer 2

Problem Analysis

We are given that a boat traveled for 2 hours against the current and 3 hours with the current, covering a total distance of 88 km. We are also told that the boat traveled 32 km more with the current than against it. We need to find the speed of the current and the speed of the boat in still water.

Solution

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

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

When the boat is traveling with the current, its effective speed is increased by the speed of the current. So the boat's speed with the current is (x + y) km/h.

We are given that the boat traveled for 2 hours against the current, covering a distance of 88 km. Using the formula distance = speed × time, we can write the equation:

(x - y) × 2 = 88 ---(1)

We are also given that the boat traveled for 3 hours with the current, covering a distance of 32 km more than when it was traveling against the current. Using the same formula, we can write the equation:

(x + y) × 3 = 88 + 32 ---(2)

Now we have a system of two equations with two variables. We can solve this system to find the values of x and y.

Solving the System of Equations

Let's solve the system of equations (1) and (2) to find the values of x and y.

From equation (1), we have:

(x - y) × 2 = 88

Expanding the equation, we get:

2x - 2y = 88 ---(3)

From equation (2), we have:

(x + y) × 3 = 88 + 32

Expanding the equation, we get:

3x + 3y = 120 ---(4)

Now we can solve equations (3) and (4) simultaneously to find the values of x and y.

To eliminate y, we can multiply equation (3) by 3 and equation (4) by 2:

6x - 6y = 264 ---(5)

6x + 6y = 240 ---(6)

Adding equations (5) and (6), we get:

12x = 504

Dividing both sides by 12, we find:

x = 42

Substituting the value of x back into equation (3), we can solve for y:

2x - 2y = 88

2(42) - 2y = 88

84 - 2y = 88

-2y = 4

Dividing both sides by -2, we find:

y = -2

Answer

The speed of the current is 2 km/h and the speed of the boat in still water is 42 km/h.