Question

Катер проплыл 72 км между пристанями по течению реки за 2 часа, а против течени-за 3 часа. За сколько часов это расстояние проплывут плоты.

Answer 1

1) 72/2 = 36 км/ч - скорость по течению
2) 72/3 = 24 км/ч - скорость против течения
3) скорость плота = скорости течения = (36 - 24)/2 = 6 км/ч
4) 72/6 = 12 часов
Ответ: за 12 часов проплывут плоты 72 км

Answer 2

Calculation of Speed and Time for the Boat

To find out how long it will take for rafts to cover the same distance, we need to calculate the speed of the boat in both directions.

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

Given that the boat traveled 72 km downstream in 2 hours, we can set up the equation:

72 km = (x + y) km/h * 2 hours Simplifying the equation, we have:

36 km/h = x + y (Equation 1)

Similarly, when the boat traveled 72 km upstream in 3 hours, we can set up the equation:

72 km = (x - y) km/h * 3 hours Simplifying the equation, we have:

24 km/h = x - y (Equation 2)

Solving the Equations

To solve the system of equations (Equation 1 and Equation 2), we can use the method of substitution or elimination. Let's use the elimination method:

Adding Equation 1 and Equation 2, we get:

(36 km/h) + (24 km/h) = (x + y) + (x - y)

Simplifying the equation, we have:

60 km/h = 2x

Dividing both sides of the equation by 2, we find:

x = 30 km/h

Substituting the value of x back into Equation 1, we can solve for y:

36 km/h = 30 km/h + y

Simplifying the equation, we have:

6 km/h = y

Calculation for the Rafts

Now that we have the speed of the boat in still water (x = 30 km/h) and the speed of the river current (y = 6 km/h), we can calculate the time it will take for the rafts to cover the same distance.

The speed of the rafts will be the difference between the speed of the boat in still water and the speed of the river current:

Speed of rafts = Speed of boat in still water - Speed of river current

Substituting the values, we have:

Speed of rafts = 30 km/h - 6 km/h = 24 km/h

To calculate the time it will take for the rafts to cover the distance, we can use the formula:

Time = Distance / Speed

Substituting the distance of 72 km and the speed of 24 km/h, we have:

Time = 72 km / 24 km/h = 3 hours

Therefore, it will take the rafts 3 hours to cover the distance of 72 km.

Please let me know if there's anything else I can help you with!