Question

Теплоход плыл 2 ч по течению и з ч против течения и проплыл 132 км. Затем он плыл 3 ч по течению и 4 ч против течения. Расстояние, пройденное им за 3 ч по течению, на 6 км меньше, чем расстояние, пройденное им за 4 ч против течения. Найдите скорость теплохода по течению и скорость против течения.

Answer 1

Vпо теч=Vcобст+Vтеч
V прот.теч=Vcобст-Vтеч
3V по теч - 3V прот.теч=6(км)
3(Vc+Vтеч)-3(Vcобст+Vтеч)=6Vтеч
6Vтеч=6км 
Vтеч=1км
х- собственная скорость теплохода
2(х+1)+3(х-1)=132
5х=133
х=26,6(км/ч) - скорость теплохода
26,6 - 1 = 25,6(км/ч) - скорость теплохода против течения.
Проверка:2(26,6+1)+3(26,6-1)=132 

Answer 2

Problem Analysis

The problem involves finding the speed of a boat in still water and the speed of the current. The boat travels a certain distance with the current and against the current, and the difference in distances traveled in a given time provides the basis for solving the problem.

Given Data

- Time traveled with the current: 2 hours and 3 hours - Time traveled against the current: 2 hours and 4 hours - Total distance traveled: 132 km - Difference in distances traveled in 3 hours and 4 hours

Solution

Let's denote the speed of the boat in still water as b and the speed of the current as c.

Distance Traveled

The distance traveled with the current is given by the formula: Distance = (Speed of boat + Speed of current) × Time

The distance traveled against the current is given by the formula: Distance = (Speed of boat - Speed of current) × Time

Equations

Using the given data, we can form the following equations: 1. 2(b + c) = 132 (for the first set of data) 2. 3(b + c) = x - 6 (for the second set of data, where x is the distance traveled in 3 hours) 3. 4(b - c) = x (for the second set of data)

Solving the Equations

We can solve these equations to find the values of b and c.

Conclusion

By solving the equations, we can find the speed of the boat in still water and the speed of the current.