Question

Помогите решить задачу, Лодка проплыла из пункта А в пункт В против течения реки 8 километров, затем вернулась обратно. Известно, что весь путь занял 2 часа. Найдите скорость лодки, если скорость течения реки 3 км/ч.

Answer 1

Пусть скорость течения реки (и плота) км/ч. Тогда скорость катера против течения равна км/ч, а по течению км/ч. Следовательно, скорость катера против течения в 3 раза больше скорости плота, а по течению — в 5 раз больше скорости плота. Если плот до встречи проплыл км, то катер — в 3 раза больше, т. е. км. После встречи катер пройдет км, а плот — в 5 раз меньше, т. е. км. Всего плот пройдет
.

Answer 2

Вроде бы 1 км в час (8:2=4-3=1)

Answer 3

Problem Analysis

We are given that a boat traveled from point A to point B against the current of a river, covering a distance of 8 kilometers. The boat then returned back to point A. The total time taken for the entire journey was 2 hours. We are also given that the speed of the river current is 3 km/h. We need to find the speed of the boat.

Solution

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

When the boat is traveling from point A to point B against the current, the effective speed of the boat is the difference between the speed of the boat in still water and the speed of the river current. So, the effective speed is (x - 3) km/h.

Similarly, when the boat is traveling from point B to point A with the current, the effective speed of the boat is the sum of the speed of the boat in still water and the speed of the river current. So, the effective speed is (x + 3) km/h.

We can use the formula distance = speed × time to calculate the time taken for each leg of the journey.

From point A to point B against the current: 8 = (x - 3) × t1 (where t1 is the time taken in hours)

From point B to point A with the current: 8 = (x + 3) × t2 (where t2 is the time taken in hours)

We are given that the total time taken for the entire journey is 2 hours: t1 + t2 = 2

We can solve these equations to find the value of x, which represents the speed of the boat in still water.

Calculation

Let's solve the equations to find the value of x.

From the equation 8 = (x - 3) × t1, we can express t1 in terms of x: t1 = 8 / (x - 3)

From the equation 8 = (x + 3) × t2, we can express t2 in terms of x: t2 = 8 / (x + 3)

Substituting the values of t1 and t2 into the equation t1 + t2 = 2, we get: 8 / (x - 3) + 8 / (x + 3) = 2

To solve this equation, we can multiply both sides by (x - 3)(x + 3) to eliminate the denominators: 8(x + 3) + 8(x - 3) = 2(x - 3)(x + 3)

Expanding and simplifying the equation: 8x + 24 + 8x - 24 = 2(x^2 - 9)

Combining like terms: 16x = 2x^2 - 18

Rearranging the equation: 2x^2 - 16x - 18 = 0

We can solve this quadratic equation using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, the values of a, b, and c are: a = 2 b = -16 c = -18

Substituting these values into the quadratic formula: x = (-(-16) ± √((-16)^2 - 4 * 2 * (-18))) / (2 * 2)

Simplifying the equation: x = (16 ± √(256 + 144)) / 4 x = (16 ± √400) / 4 x = (16 ± 20) / 4

We have two possible solutions for x: x1 = (16 + 20) / 4 = 9 x2 = (16 - 20) / 4 = -1

Since the speed of the boat cannot be negative, we discard the solution x2 = -1.

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

Answer

The speed of the boat is 9 km/h.