Question

ПОЖАЛУЙСТА. Катер шел по течению реки 180 км, а затем вернулся обратно, причем на обратный путь было затрачено на 8 часов больше. Скорость течения реки равна 4 км/ч. Найди собственную скорость катера (в км/ч)

Answer 1

Ответ:

14

Пошаговое объяснение:

x - скорость катера, км/ч.

180/(x-4) -180/(x+4)=8                         |4

(45(x+4-x+4))/((x-4)(x+4))=2

360=2(x²-16)

x²-16=360/2

x²=180+16

x=√196

x=14 км/ч

Answer 2

Problem Analysis

We are given that a boat traveled 180 km downstream and then returned upstream, taking 8 hours longer for the return trip. The speed of the river current is given as 4 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 downstream, its effective speed is increased by the speed of the river current. So the boat's speed downstream is (x + 4) km/h.

When the boat is traveling upstream, its effective speed is decreased by the speed of the river current. So the boat's speed upstream is (x - 4) km/h.

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

1. Downstream journey: - Distance = 180 km - Speed = (x + 4) km/h - Time = Distance / Speed

2. Upstream journey: - Distance = 180 km - Speed = (x - 4) km/h - Time = Distance / Speed

According to the problem, the time taken for the upstream journey is 8 hours longer than the time taken for the downstream journey. So we can set up the equation:

(Time upstream) = (Time downstream) + 8

Substituting the values we calculated earlier:

(180 / (x - 4)) = (180 / (x + 4)) + 8

Now we can solve this equation to find the value of x, which represents the speed of the boat in still water.

Calculation

Let's solve the equation:

(180 / (x - 4)) = (180 / (x + 4)) + 8

To simplify the equation, we can multiply both sides by (x - 4)(x + 4) to eliminate the denominators:

180(x + 4) = 180(x - 4) + 8(x - 4)(x + 4)

Expanding and simplifying:

180x + 720 = 180x - 720 + 8(x^2 - 16)

Simplifying further:

180x + 720 = 180x - 720 + 8x^2 - 128

Rearranging the terms:

8x^2 - 128 = 0

Dividing both sides by 8:

x^2 - 16 = 0

Factoring:

(x - 4)(x + 4) = 0

Solving for x:

x - 4 = 0 --> x = 4

x + 4 = 0 --> x = -4

Since the speed of the boat cannot be negative, we discard the solution x = -4.

Therefore, the speed of the boat in still water is 4 km/h.

Answer

The speed of the boat in still water is 4 km/h.