Question

По озеру теплоход проходит некоторое расстояние за 4 часа,а по течению реки он проходит такое же расстояние за 3 часа.За сколько часов теплоход пройдет то же расстояние против течения реки?ПЛИИИЗЗ

Answer 1

Пусть скорость теплохода х км/час, скорость течения у км/час

за 4 часа по озеру- значит со скоростью х км/час
за 3 часа по течению- значит со скоростью х+у

расстояние одно и тоже.

составим уравнение

$\displaystyle 4x=3(x+y) 4x=3x+3y x=3y$

теперь обозначим время против течения за t а скорость будет х-у
путь один и тот же

составим уравнение

$\displaystyle 4x=t(x-y)$

заменим х=3у

$\displaystyle 4*(3y)=t(3y-y) 12y=t*(2y) t= 12y:2y t=6$

Время движения против течения реки составит 6 час
 

Answer 2

Problem Analysis

The problem involves a boat traveling a certain distance in still water and then traveling the same distance with the current of a river. We need to determine how long it will take for the boat to travel the same distance against the current of the river.

Given Information

- The boat travels a certain distance in 4 hours in still water. - The boat travels the same distance with the current of the river in 3 hours.

Solution

Let's denote the speed of the boat in still water as b and the speed of the current as c. - When the boat travels with the current, its effective speed is b + c. - When the boat travels against the current, its effective speed is b - c.

We can use the formula: time = distance / speed to solve for the speed of the boat in still water and the speed of the current.

Calculation

1. From the given information, we have: - 4(b + c) = distance - 3(b - c) = distance

2. Solving for b and c: - 4(b + c) = 3(b - c) - 4b + 4c = 3b - 3c - b = 7c

3. Now, we need to find the time it takes for the boat to travel the same distance against the current of the river. - Let's denote this time as t.

Using the formula time = distance / speed, we have: - distance = speed * time - distance = (b - c) * t

Substituting b = 7c: - distance = 6c * t

Since the distance is the same as before, we can equate it to the distance traveled with the current: - 4(b + c) = 6c * t

Solving for t: - 4(7c + c) = 6c * t - 32c = 6c * t - t = 32c / 6c - t = 16/3 hours

Answer

So, the boat will take 16/3 hours to travel the same distance against the current of the river.