Question

Лодка прошла 3 ч по течению реки и 7 ч против течения, проплыв за всё это время 62 км. Скорость течения реки 2 км/ч. Найдите собственную скорость лодки. Решите задачу методом составления уравнения. Заранее спасибо!!!

Answer 1

3*(x+2)+7(x-2)=62
3x+6+7x-14=62
10x-8=62
10x=62+8
10x=70
x=70:10
x=7км/ч собственная скорость лодки. 

Answer 2

Problem Analysis

We are given that a boat traveled downstream for 3 hours and upstream for 7 hours, covering a total distance of 62 km. The speed of the river's current is 2 km/h. We need to find the speed of the boat.

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

Downstream Journey

During the downstream journey, the boat's speed is increased by the speed of the river's current. So, the effective speed of the boat is (x + 2) km/h.

The time taken for the downstream journey is 3 hours, and the distance covered is 62 km. We can use the formula distance = speed × time to write the equation:

(x + 2) × 3 = 62

Upstream Journey

During the upstream journey, the boat's speed is decreased by the speed of the river's current. So, the effective speed of the boat is (x - 2) km/h.

The time taken for the upstream journey is 7 hours, and the distance covered is 62 km. We can use the same formula to write the equation:

(x - 2) × 7 = 62

Solving the Equations

Now, we have two equations with two unknowns. We can solve these equations simultaneously to find the value of x, which represents the speed of the boat in still water.

Let's solve the equations:

(x + 2) × 3 = 62

(x - 2) × 7 = 62

Expanding the equations:

3x + 6 = 62

7x - 14 = 62

Simplifying the equations:

3x = 56

7x = 76

Solving for x:

x = 56/3 ≈ 18.67

Answer

The speed of the boat in still water is approximately 18.67 km/h.

Verification

Let's verify our answer using the given information.

During the downstream journey, the boat's speed is (18.67 + 2) ≈ 20.67 km/h. The time taken is 3 hours, so the distance covered is 20.67 × 3 = 62 km.

During the upstream journey, the boat's speed is (18.67 - 2) ≈ 16.67 km/h. The time taken is 7 hours, so the distance covered is 16.67 × 7 = 116.69 km.

The total distance covered is 62 km + 116.69 km = 178.69 km, which matches the given information.

Therefore, our answer is verified.

Conclusion

The speed of the boat in still water is approximately 18.67 km/h.