Question

Лодка прошла 120км за тичением реки и вернулся назад , потратил на весь путь 11 часов. Найдите скорость тичения , если собственная скорость лодки 22км/час.

Answer 1

Problem Analysis

We are given that a boat traveled 120 km downstream and then returned upstream, taking a total of 11 hours for the entire journey. We need to find the speed of the river current, given that the boat's own speed is 22 km/h.

Solution

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

When the boat is traveling downstream, it benefits from the speed of the river current, so its effective speed is the sum of its own speed and the speed of the current. Therefore, the boat's effective speed downstream is (22 + x) km/h.

When the boat is traveling upstream, it has to overcome the speed of the river current, so its effective speed is the difference between its own speed and the speed of the current. Therefore, the boat's effective speed upstream is (22 - x) km/h.

We are given that the boat traveled a total distance of 120 km. Since the distance traveled downstream is the same as the distance traveled upstream, we can set up the following equation:

120 km = (22 + x) km/h * t1 + (22 - x) km/h * t2

where t1 is the time taken to travel downstream and t2 is the time taken to travel upstream.

We are also given that the total time for the journey is 11 hours:

t1 + t2 = 11 hours

We have two equations with two unknowns, so we can solve this system of equations to find the value of x, the speed of the river current.

Let's solve the equations:

120 = (22 + x) * t1 + (22 - x) * t2 (Equation 1)

t1 + t2 = 11 (Equation 2)

To solve this system of equations, we need another equation. Unfortunately, the given information does not provide any additional equations. Therefore, we cannot determine the exact value of the river current speed without additional information.

If you have any additional information or constraints, please let me know, and I'll be happy to help further.