Question

Расстояние между двумя пунктами катер проплывает по озеру за 3 ч. Такое же расстояние по реке плот проплыват за 12 ч. За сколько часов катер проплывает такое же расстояние, если он плывет по течению реки ?

Answer 1

1. Примем расстояние как "х"
2. Скорость катера по озеру Vк-о = х/3 км/час
3. Скорость реки   Vр = х/12 км/час
4. Скорость катера при движении по течению реки 
Vк-р = Vк-о +Vр = (х/3) + (х/12) =  5х/12  км/час
5. Время движения катера по течению реки (путь делим на скорость)
Т = х:(5х/12) = (х·12)/5х = 12/5 = 2,4 часа
Ответ. 2,4 часа

Answer 2

Problem Analysis

We are given that a boat can travel a certain distance on a lake in 3 hours, and a raft can travel the same distance on a river in 12 hours. We need to determine how long it would take for the boat to travel the same distance on the river, assuming it is moving with the current.

Solution

Let's assume that the distance between the two points is d.

We are given that the boat can travel the distance d on the lake in 3 hours. Therefore, the speed of the boat on the lake is d/3.

We are also given that the raft can travel the same distance d on the river in 12 hours. Therefore, the speed of the raft on the river is d/12.

When the boat is moving with the current, its effective speed will be the sum of its speed on the lake and the speed of the current. Let's assume the speed of the current is c.

Therefore, the effective speed of the boat when moving with the current is d/3 + c.

Since speed is equal to distance divided by time, we can set up the following equation:

d = (d/3 + c) * t

where t is the time it takes for the boat to travel the distance d on the river.

Simplifying the equation, we get:

3d = d + 3ct

Solving for t, we get:

t = (3d - d) / (3c) = 2d / (3c)

Therefore, it would take the boat 2d / (3c) hours to travel the same distance on the river, assuming it is moving with the current.

Answer

If the boat is moving with the current of the river, it would take the boat 2d / (3c) hours to travel the same distance, where d is the distance between the two points and c is the speed of the current.