Question

Лодка шла 3ч ПРОТИВ течения реки и 2 ч ПО течению,пройдя за всё время 37 км. скорость течения реки 3км/ч.найдите собственную скорость лодки.решите задачу составив уравнение.

Answer 1

Х - собственная скорость лодки
х+3 - скорость по течению
х-3 - скорость против течения
3(х-3)+2(х+3)=37
3х-9+2х+6=37
5х=37+9-6
5х=40
х=40:5
х=8 (км/час) скорость лодки
Ответ: собственная скорость лодки равна 8 км/час

Answer 2

Problem Analysis

To solve this problem, we need to find the speed of the boat in still water. We are given that the boat traveled for 3 hours against the current of the river and 2 hours with the current, covering a total distance of 37 km. The speed of the river's current is given as 3 km/h.

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

Solution

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

1. Against the current: - The speed of the boat relative to the river's current is (x - 3) km/h. - The time taken to travel against the current is 3 hours. - Therefore, the distance traveled against the current is (x - 3) × 3 km.

2. With the current: - The speed of the boat relative to the river's current is (x + 3) km/h. - The time taken to travel with the current is 2 hours. - Therefore, the distance traveled with the current is (x + 3) × 2 km.

3. Total distance: - The total distance traveled is given as 37 km. - Therefore, we can write the equation: (x - 3) × 3 + (x + 3) × 2 = 37.

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 have: 3x - 9 + 2x + 6 = 37

Combining like terms, we get: 5x - 3 = 37

Adding 3 to both sides, we get: 5x = 40

Dividing both sides by 5, we get: x = 8

Answer

The speed of the boat in still water is 8 km/h.

Verification

To verify our answer, let's substitute the value of x into the equation and check if both sides are equal.

Left-hand side: (x - 3) × 3 + (x + 3) × 2 = (8 - 3) × 3 + (8 + 3) × 2 = 5 × 3 + 11 × 2 = 15 + 22 = 37

Right-hand side: 37 = 37

Since both sides are equal, our answer of x = 8 km/h is correct.

Conclusion

The speed of the boat in still water is 8 km/h.