Question

Катер пройшов відстань між пристанями за течією річки за 2 год., а назад - за 3 год. Знайдіть швидкість катера, якщо швидкість течії річки 2 км/год.

Answer 1

3*(х-2)=2*(х+2)
3х-6=2х+4
3х-2х=4+6
х=10км/год - швидкысть

Answer 2

Calculation of the Boat's Speed

To find the speed of the boat, we can use the formula:

Speed of the boat = Distance / Time

Let's denote the speed of the boat as 'v' and the speed of the river's current as 'c'. We are given that the speed of the current is 2 km/h.

According to the problem, the boat took 2 hours to travel downstream (with the current) between the two ports and 3 hours to travel upstream (against the current) between the same two ports.

Let's assume the distance between the ports is 'd' km.

When the boat is moving downstream, its effective speed is the sum of its own speed and the speed of the current. Therefore, the boat's speed downstream is 'v + c'.

When the boat is moving upstream, its effective speed is the difference between its own speed and the speed of the current. Therefore, the boat's speed upstream is 'v - c'.

Using the formula mentioned earlier, we can set up the following equations:

Downstream speed equation: (v + c) = d / 2

Upstream speed equation: (v - c) = d / 3

We can solve these two equations simultaneously to find the values of 'v' and 'd'.

Let's solve the equations:

(v + c) = d / 2 ----(1)

(v - c) = d / 3 ----(2)

Adding equations (1) and (2), we get:

2v = (d / 2) + (d / 3)

Multiplying both sides by 6 to eliminate the denominators, we have:

12v = 3d + 2d

12v = 5d

Dividing both sides by 5, we get:

v = (5d) / 12

Now, we can substitute the given value of the speed of the current, which is 2 km/h, into the equation:

v = (5d) / 12

v = (5 * 2) / 12

v = 10 / 12

v = 5 / 6 km/h

Therefore, the speed of the boat is 5/6 km/h.

Please note that the distance between the ports, 'd', was not provided in the question. Without this information, we cannot calculate the exact speed of the boat.