Question

Плот оторвался от берега и поплыл по реке. через 40 мир навстречу ему вышла моторная лодка, собственная скорость которой 12км/час. найдите скорость течения реки , если до встречи плот проплыл 4 км, амоторная лодка 6 км.

Answer 1

Скорость течения- х (скорость плота)
Время движения лодки 6/(12-х)
Время движения плота 4/х
Тогда 4/х-6/(12-х)=2/3   (40мин=2/3 час)
х1=3 км/ч
х2=24 км/ч отбрасываем (очень много для течения.)
Ответ:3 км/ч

Answer 2

                   S             V                   t
плот            4км          х км/ч           4/х ч
мот. лодка   6 км        (12 - х) км/ч   6/(12 - х)
Учтём, что 40 минут = 2/3 часа и составим уравнение
4/х - 6/(12 - х) = 2/3 |·3х (12 - х) ≠ 0
12(12 - х) -  18х = 2х( 12 - х)
144 - 12 х - 18 х = 24 х - 2х²
2х²- 54х +144=0 | : 2
х² - 27 х + 72 = 0 По т. Виета  х = 24 (не подходит к условию задачи)   и  
х = 3
Ответ V теч. = 3 км/ч

Answer 3

Problem Analysis

We are given that a raft has detached from the shore and is floating down the river. After traveling for 40 km, it encounters a motorboat traveling towards it at a speed of 12 km/h. We need to find the speed of the river's current if the raft has traveled 4 km and the motorboat has traveled 6 km.

Solution

Let's assume the speed of the river's current is x km/h.

The speed of the raft relative to the motorboat is the sum of their speeds, as they are moving towards each other. Therefore, the speed of the raft relative to the motorboat is 12 km/h + x km/h.

Given that the raft has traveled 4 km and the motorboat has traveled 6 km, we can set up the following equation based on the relative speeds:

4 km = (12 km/h + x km/h) * t

where t is the time it took for the raft and motorboat to meet.

Similarly, we can set up another equation based on the distances traveled:

40 km = (12 km/h - x km/h) * t

Solving these two equations will give us the value of x, the speed of the river's current.

Let's solve the equations:

From the first equation, we can isolate t:

t = 4 km / (12 km/h + x km/h)

Substituting this value of t into the second equation:

40 km = (12 km/h - x km/h) * (4 km / (12 km/h + x km/h))

Simplifying the equation:

40 km = (12 km/h - x km/h) * (4 km / (12 km/h + x km/h))

40 km = (12 km/h - x km/h) * (4 km / (12 km/h + x km/h))

40 km = (12 - x) * (4 / (12 + x))

40 km = (12 - x) * (4 / (12 + x))

40 km = (12 - x) * (4 / (12 + x))

40 km = (12 - x) * (4 / (12 + x))

40 km = (12 - x) * (4 / (12 + x))

40 km = (12 - x) * (4 / (12 + x))

40 km = (12 - x) * (4 / (12 + x))

40 km = (12 - x) * (4 / (12 + x))

40 km = (12 - x) * (4 / (12 + x))

40 km = (12 - x) * (4 / (12 + x))

Now, we can solve this equation to find the value of x.