Question

Катер провлывает путь от А до Б за 3 часа,а плот за 12 часов. За сколько часов катер проплывёт путь от Б до А

Answer 1

К-скорость катера в стоячей воде, п - скорость плота(она же скорость реки)
все три события плывут одно и то же расстояние, с разным временем и разной скоростью
(к+п) - по течению катер, (к-п) - катер против течения
3*(к+п)=12*п=х*(к-п)
из первого равно находим отношение скоростей (собственной катера и плота)
3к=9п
к=3п
выражаем скорость катера против течения, тоже через скорость плота
к-п=2п
и из второго равенства (не забываем, что расстояние от А до Б не изменилось)
12п=2пх
х=6
Ответ: 6 часов

Answer 2

To solve this problem, we can use the concept of relative speed. When two objects are moving towards each other, their speeds are additive, and when they are moving away from each other, their speeds are subtractive.

Let's assume that the distance between points A and B is D (same for the boat and the raft).

Speed of the boat (let's call it B) = Distance (D) / Time (3 hours) = D/3. Speed of the raft (let's call it R) = Distance (D) / Time (12 hours) = D/12.

When the boat travels from A to B, its speed is B. When the boat travels from B to A, its speed becomes -B (opposite direction).

Now, to find the time it takes for the boat to travel from B to A, we can use the formula:

Time = Distance / Speed.

Time taken by the boat to travel from B to A = D / (-B).

Substitute the values:

Time taken by the boat to travel from B to A = D / (-(D/3)) = -3 hours.

The negative sign indicates that the boat is traveling in the opposite direction. However, time cannot be negative, so we take the absolute value, making it 3 hours.

So, the boat will take 3 hours to travel from B to A.