Question

Лодка шла 3 часа по течению реки и 7 часов против течения реки, проплыв за все это время 62 км. Скорость течения реки 2 км/ч. Найдите собственную скорость лодки. Задачу решите уравнением

Answer 1

4(х+2)+5х=71
4х+8+5х=71
9х=63
Х=7 скорость лодки

Answer 2

Problem Analysis

We are given that a boat traveled for 3 hours with the current of a river and 7 hours against the current, covering a total distance of 62 km. The speed of the river current is given as 2 km/h. We need to find the speed of the boat in still water.

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.

Let's calculate the distance traveled by the boat with the current and against the current.

1. Distance traveled with the current: - Speed of the boat with the current = (x + 2) km/h (since the current adds to the speed of the boat) - Time = 3 hours - Distance = (x + 2) × 3 km

2. Distance traveled against the current: - Speed of the boat against the current = (x - 2) km/h (since the current subtracts from the speed of the boat) - Time = 7 hours - Distance = (x - 2) × 7 km

According to the problem, the total distance traveled is 62 km. So we can set up the equation:

(x + 2) × 3 + (x - 2) × 7 = 62

Now, let's solve this equation to find the value of x.

Solving the Equation

Expanding the equation, we get:

3x + 6 + 7x - 14 = 62

Combining like terms, we have:

10x - 8 = 62

Adding 8 to both sides of the equation, we get:

10x = 70

Dividing both sides of the equation by 10, we get:

x = 7

Answer

The speed of the boat in still water is 7 km/h.

Verification

Let's verify our answer by substituting the value of x into the equation:

(7 + 2) × 3 + (7 - 2) × 7 = 62

Simplifying the equation, we get:

9 × 3 + 5 × 7 = 62

27 + 35 = 62

62 = 62

The equation is true, which confirms that our answer is correct.