Question

Лодка шла по течению реки 2,8 ч и против течения 3,4 ч. Путь, пройденный лодкой по течению, оказался на 4,4 км короче пути, пройденного против течения. Найти скорость лодки по реке, если скорость течения реки равна 2 км/ч.

Answer 1

Фразу "скорость лодки по реке" я понимаю, как скорость лодки по течению реки, но на всякий случай определю и скорость проив течения, и скорость в стоячей воде. так что выбор за Вами.

Пусть скорость лодки в стоячей воде х км/ч, тогда скорость лодки по течению (х + 2) км/ч, а против течения (х - 2) км/ч.

Путь, пройденный по течению за 2,8 часа равен 2,8(х + 2)км,путь, пройденный против течения за 3,4 часа равен 3,4(х - 2)км. что на 4,4 км больше, чем по течению.

Уравнение 3,4(х - 2) - 2,8(х + 2) = 4,4

Решаем уравнение

3,4х - 6,8 - 2,8х - 5,6 = 4,4

0,6х = 16,8

х = 28(км/ч0 - собственная скорость лодки.

х + 2 = 30км/ч - скорость лодки по течению

х - 2 = 26км/ч - скорость лодки против течения.

Ответ: скорость лодки при движении по течению реки равна 30км/ч

Answer 2

Problem Analysis

We are given the following information: - The boat traveled downstream for 2.8 hours. - The boat traveled upstream for 3.4 hours. - The distance traveled downstream is 4.4 km less than the distance traveled upstream. - The speed of the river current is 2 km/h.

We need to find the speed of the boat in still water.

Downstream Speed Calculation

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

When the boat is traveling downstream, its effective speed is the sum of its speed in still water and the speed of the river current. Therefore, the effective speed downstream is (x + 2) km/h.

The distance traveled downstream is the product of the effective speed and the time taken: (x + 2) * 2.8 km.

Upstream Speed Calculation

When the boat is traveling upstream, its effective speed is the difference between its speed in still water and the speed of the river current. Therefore, the effective speed upstream is (x - 2) km/h.

The distance traveled upstream is the product of the effective speed and the time taken: (x - 2) * 3.4 km.

Equation Setup

We are given that the distance traveled downstream is 4.4 km less than the distance traveled upstream. Therefore, we can set up the following equation:

(x + 2) * 2.8 = (x - 2) * 3.4 + 4.4

Solving the Equation

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

(x + 2) * 2.8 = (x - 2) * 3.4 + 4.4

Expanding the equation:

2.8x + 5.6 = 3.4x - 6.8 + 4.4

Combining like terms:

2.8x + 5.6 = 3.4x - 2.4

Moving all terms involving x to one side:

2.8x - 3.4x = -2.4 - 5.6

Simplifying:

-0.6x = -8

Dividing both sides by -0.6:

x = 8 / 0.6

Calculating:

x = 13.33

Answer

The speed of the boat in still water is 13.33 km/h.

Verification

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

(13.33 + 2) * 2.8 = (13.33 - 2) * 3.4 + 4.4

Calculating:

15.33 * 2.8 = 11.33 * 3.4 + 4.4

42.924 = 38.522 + 4.4

42.924 = 42.922

The equation holds true, verifying that the speed of the boat in still water is indeed 13.33 km/h.