Question

Лодка шла по течению 3 ч и против 5 ч. Путь пройденный лодкой по течению,оказался на 7 км длиннее пути,пройденного против течения найдите скорость лодки в стоячей воде,если скорость течения реки 4км/ч РЕШИТЕ УРАВНЕНИЕМ!!!

Answer 1

Х скорость в стоячей воде
х+4 скорость по течению
х-4 скорость против течения
3(х+4)-5(х-4)=7
3х+12-5х+20=7
-2х=-25
х=12,5 км/ч скорость в стоячей воде

Answer 2

Problem Analysis

We are given that a boat traveled downstream for 3 hours and upstream for 5 hours. The distance covered by the boat downstream is 7 km longer than the distance covered upstream. We need to find the speed of the boat in still water, given that the speed of the river current is 4 km/h.

Solution

Let's assume the speed of the boat in still water is x km/h. Since the boat is traveling downstream, its effective speed will be the sum of its speed in still water and the speed of the river current. Therefore, the effective speed downstream is (x + 4) km/h.

Similarly, when the boat is traveling upstream, its effective speed will be the difference between its speed in still water and the speed of the river current. Therefore, the effective speed upstream is (x - 4) km/h.

We are given that the boat traveled downstream for 3 hours and upstream for 5 hours. Let's calculate the distances covered in each case.

The distance covered downstream is given by the formula: distance = speed × time. Therefore, the distance covered downstream is (x + 4) × 3 km.

The distance covered upstream is given by the formula: distance = speed × time. Therefore, the distance covered upstream is (x - 4) × 5 km.

We are also given that the distance covered downstream is 7 km longer than the distance covered upstream. Therefore, we can set up the following equation:

(x + 4) × 3 = (x - 4) × 5 + 7

Now, let's solve this equation to find the value of x, which represents the speed of the boat in still water.

Solving the Equation

Expanding the equation, we get:

3x + 12 = 5x - 20 + 7

Simplifying the equation, we get:

3x + 12 = 5x - 13

Rearranging the equation, we get:

2x = 25

Dividing both sides of the equation by 2, we get:

x = 12.5

Therefore, the speed of the boat in still water is 12.5 km/h.

Answer

The speed of the boat in still water is 12.5 km/h.

Verification

Let's verify our answer by substituting the value of x into the equation and checking if both sides are equal.

Substituting x = 12.5 into the equation, we get:

(12.5 + 4) × 3 = (12.5 - 4) × 5 + 7

Simplifying both sides of the equation, we get:

16.5 × 3 = 8.5 × 5 + 7

49.5 = 42.5 + 7

49.5 = 49.5

Both sides of the equation are equal, which verifies that our answer is correct.

Conclusion

The speed of the boat in still water is 12.5 km/h.