Question

Лодка шла против течения реки 4,5 часа и по течению 2 , 1 часа. Найдите скорость лодки в стоячей воде , если она шла всего 52 , 2 км , а скорость течения реки равна 3 км/час.

Answer 1

Пусть скорость лодки в стоячей воде х км/ч . Составим уравнение: 4,5 (х - 3) + 2,1 (х + 3) = 52,2; 4,5х - 13,5 + 2,1х + 6,3 = 52,2; 6,6х - 7,2 = 52,2; 6,6х = 52,2 + 7,2; 6,6х = 59,4; х = 9. Ответ: скорость лодки в стоячей воде 9 км/ч .

Answer 2

Problem Analysis

We are given that a boat traveled against the current of a river for 4.5 hours and with the current for 2.1 hours. The total distance traveled by the boat is 52.2 km, and the speed of the river current is 3 km/h. We need to find the speed of the boat in still water.

Solution

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

When the boat is traveling against the current, the effective speed is reduced by the speed of the current. So, the speed of the boat against the current is (x - 3) km/h.

When the boat is traveling with the current, the effective speed is increased by the speed of the current. So, the speed of the boat with the current is (x + 3) km/h.

We can use the formula distance = speed × time to calculate the distances traveled in each case.

The distance traveled against the current is (x - 3) × 4.5 km, and the distance traveled with the current is (x + 3) × 2.1 km.

According to the problem, the total distance traveled is 52.2 km. So, we can write the equation:

(x - 3) × 4.5 + (x + 3) × 2.1 = 52.2

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

Calculation

Expanding the equation, we get:

4.5x - 13.5 + 2.1x + 6.3 = 52.2

Combining like terms, we have:

6.6x - 7.2 = 52.2

Adding 7.2 to both sides of the equation, we get:

6.6x = 59.4

Dividing both sides of the equation by 6.6, we get:

x = 9

Answer

The speed of the boat in still water is 9 km/h.

Verification

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

(9 - 3) × 4.5 + (9 + 3) × 2.1 = 52.2

Simplifying the equation, we have:

6 × 4.5 + 12 × 2.1 = 52.2

27 + 25.2 = 52.2

52.2 = 52.2

The equation is true, which confirms that the speed of the boat in still water is indeed 9 km/h.