Question

От пристани A до пристани B катер плывёт по реке 15 минут,а обратно - 20 минут. Найти скорость течения реки,если собственная скорость катера 14 км/ч

Answer 1

Путь катера по течению находим по формуле S = (Uк+Uт)t, а против течения S = (Uк-Uт)t
Так как расстояние равно, приравниваем эти 2 формулы:
(Uк+Uт)t = (Uк-Uт)t
(Uк+Uт)*15 = (Uк-Uт)*20
15Uк+15Uт-20Uк+20Uт = 0
-5Uк+35Uт = 0
35Uт = 5Uк
Uт = 5*14/35 = 2 км/ч
Ответ: 2 км/ч

Answer 2

Problem Analysis

We are given that a boat travels from port A to port B on a river in 15 minutes, and the return journey takes 20 minutes. We need to find the speed of the river's current, given that the boat's own speed is 14 km/h.

Solution

Let's assume the speed of the river's current is v km/h.

When the boat is traveling from port A to port B, it is moving against the current. Therefore, the effective speed of the boat is the difference between its own speed and the speed of the current: 14 - v km/h.

Similarly, when the boat is traveling from port B to port A, it is moving with the current. Therefore, the effective speed of the boat is the sum of its own speed and the speed of the current: 14 + v km/h.

We can use the formula speed = distance / time to calculate the distance traveled by the boat in each direction.

Let's denote the distance between port A and port B as d km.

From the given information, we have the following equations:

1. Distance from A to B: d = (14 - v) * (15/60) (since the time is given in minutes) 2. Distance from B to A: d = (14 + v) * (20/60) (since the time is given in minutes)

We can solve these equations to find the value of v.

Calculation

Let's calculate the value of v using the given equations.

From equation 1, we have: d = (14 - v) * (15/60)

Simplifying, we get: d = (14 - v) * (1/4)

Multiplying both sides by 4, we get: 4d = 14 - v

From equation 2, we have: d = (14 + v) * (20/60)

Simplifying, we get: d = (14 + v) * (1/3)

Multiplying both sides by 3, we get: 3d = 14 + v

Now we have a system of equations: 4d = 14 - v 3d = 14 + v

We can solve this system of equations to find the value of v.

Subtracting the second equation from the first equation, we get: 4d - 3d = 14 - v - (14 + v)

Simplifying, we get: d = -2v

Since d cannot be negative, we can conclude that v = 0.

Answer

The speed of the river's current is 0 km/h. This means that there is no current in the river, and the boat's speed remains constant at 14 km/h regardless of the direction of travel.

Please let me know if I can help you with anything else.