Question

Катер проплыл 72 км между пристанями по течению за 2 ч,а против течения за 3 ч.За сколько часов это расстояние проплывут плоты?

Answer 1

Пусть течение реки у км/ч,

скорость катера х км/ч .

По течению:

72/(х+у)=2

Против течения:

72/(х-у)=3

Их первого уравнеия выразим х:

72=2(х+у)

36=х+у

х=36-у

Подставим во второе уравнение:

72/(36-у-у)=3

72=3(36-2у)

24=36-2у

2у=36-24

2у=12

у=6км/ч - скорость течения

х= 36-6=30км/ч - скорость катера

Плот Плывет только по течению и со скоростью течения реки.

72/6=12 часов

Ответ. 12 часов 

Answer 2

Скорость катера по течению 72/2-  36 км/ч

Скорость катера против течения  72/3= 24 км /ч 2 скорости течения

само течение реки (36-24)/2=  6 км/ч

Плот плывет со скоростью течения 6км/ ч

и потребуется 72/6=  12 часов

Ответ 12

Answer 3

Calculation of Time to Travel the Distance

To calculate the time it takes for the rafts to travel the given distance, we need to determine the speed of the rafts in still water. We can do this by finding the difference between the speed of the boat when traveling with the current and against the current.

Let's assume the speed of the boat in still water is x km/h and the speed of the current is y km/h.

When the boat is traveling with the current, its effective speed is the sum of the speed of the boat and the speed of the current. Therefore, the effective speed is (x + y) km/h.

Similarly, when the boat is traveling against the current, its effective speed is the difference between the speed of the boat and the speed of the current. Therefore, the effective speed is (x - y) km/h.

We are given that the boat traveled a distance of 72 km between the two docks in 2 hours when traveling with the current, and in 3 hours when traveling against the current.

Using the formula distance = speed × time, we can set up the following equations:

1. When traveling with the current: 72 = (x + y) × 2 2. When traveling against the current: 72 = (x - y) × 3

To solve these equations, we can use the method of substitution or elimination. Let's use the method of substitution.

From equation 1, we can express x in terms of y as follows:

x = 72/2 - y = 36 - y

Substituting this value of x into equation 2, we get:

72 = (36 - y - y) × 3

Simplifying the equation:

72 = (36 - 2y) × 3

72 = 108 - 6y

Rearranging the equation:

6y = 108 - 72

6y = 36

y = 36/6

y = 6

Now that we have the value of y, we can substitute it back into equation 1 to find the value of x:

x = 36 - y = 36 - 6 = 30

Therefore, the speed of the boat in still water is 30 km/h and the speed of the current is 6 km/h.

Time for the Rafts to Travel the Distance

Now that we know the speed of the rafts in still water, we can calculate the time it takes for the rafts to travel the given distance.

The speed of the rafts when traveling with the current is the sum of the speed of the rafts and the speed of the current, which is (30 + 6) km/h = 36 km/h.

Using the formula distance = speed × time, we can calculate the time it takes for the rafts to travel the distance:

72 km = 36 km/h × time

Simplifying the equation:

time = 72 km / 36 km/h

time = 2 hours

Therefore, it will take the rafts 2 hours to travel the distance of 72 km.