Question

Катер проплывает некоторое расстояние по озеру за 6 ч, а по течению реки за 5 ч. Сколько времени потребуется плоту, чтобы проплыть такое же расстояние по реке? Ответь СРОЧНО!!!!!

Answer 1

Пусть расстояние 1. Тогда скорость катера в стоячей воде $\frac16$ км/ч., а по реке $\frac15$ км/ч. Разность этих скоростей - скорость течения реки, с которой плывёт плот.
$\frac15-\frac16=\frac{6-5}{30}=\frac1{30}$ км/ч - скорость плота.
Значит, плот пройдёт то же расстояние за 30 ч.

Answer 2

Problem Analysis

We are given that a boat can travel a certain distance across a lake in 6 hours and the same distance along the current of a river in 5 hours. We need to determine how long it will take a raft to travel the same distance downstream in the river.

Solution

Let's assume that the distance the boat travels is d.

We can use the formula: speed = distance / time.

The speed of the boat in still water is given by: speed_boat = d / 6.

The speed of the boat along the current of the river is given by: speed_boat_river = d / 5.

The speed of the current of the river is the difference between the speed of the boat in still water and the speed of the boat along the current: speed_current = speed_boat - speed_boat_river.

Now, we can calculate the time it will take for the raft to travel the same distance downstream in the river using the formula: time_raft = d / (speed_boat + speed_current).

Let's substitute the values and calculate the time it will take for the raft to travel the same distance downstream in the river.

Calculation

Given: - Boat travel time across the lake: 6 hours - Boat travel time along the current of the river: 5 hours

Let's assume the distance the boat travels is d.

The speed of the boat in still water is given by: speed_boat = d / 6.

The speed of the boat along the current of the river is given by: speed_boat_river = d / 5.

The speed of the current of the river is the difference between the speed of the boat in still water and the speed of the boat along the current: speed_current = speed_boat - speed_boat_river.

The time it will take for the raft to travel the same distance downstream in the river is given by: time_raft = d / (speed_boat + speed_current).

Substituting the values, we have:

time_raft = d / (d / 6 + (d / 6 - d / 5))

Simplifying the expression, we get:

time_raft = d / (d / 6 + d / 6 - d / 5)

time_raft = d / (2d / 6 - d / 5)

time_raft = d / (d(2/6 - 1/5))

time_raft = d / (d(10/30 - 6/30))

time_raft = d / (d(4/30))

time_raft = 30 / 4

time_raft = 7.5 hours

Therefore, it will take the raft 7.5 hours to travel the same distance downstream in the river.

Answer

The raft will take 7.5 hours to travel the same distance downstream in the river.

Please note that the above solution assumes a constant speed for the boat and the current. In reality, the speed of the current may vary, which could affect the actual time taken by the raft to travel the same distance downstream in the river.