Question

Помогите решить! Расстояние,равное 3,6 км,проплыли по течению за 30 мин.,а против течения за 40 минут.Определите скорость течения реки.За сколько часов это же расстояние проплывут плоты?

Answer 1

S = v * t - формула пути
s = 3,6 км - расстояние    
t = 30 мин = 0,5 ч - время в пути по течению реки
t = 40 мин = 2/3 ч - время в пути против течения реки
v - ? - скорость течения реки
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1) 3,6 : 0,5 = 7,2 (км/ч) - скорость по течению реки;
2) 3,6 : 2/3 = 36/10 * 3/2 = (18*3)/(10*1) = 54/10 = 5,4 (км/ч) - скорость против течения реки;
3) (7,2 - 5,4) : 2 = 1,8 : 2 = 0,9 (км/ч) - скорость течения реки = скорости плота;
4) 3,6 : 0,9 = 4 (ч) - за 4 часа плоты проплывут 3,6 км.
Ответ: 0,9 км/ч; 4 ч.

Answer 2

Problem Analysis

We are given that a distance of 3.6 km is covered in 30 minutes when traveling with the current and in 40 minutes when traveling against the current. We need to determine the speed of the river's current and the time it would take for rafts to cover the same distance.

Solution

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

When traveling with the current, the effective speed of the boat is the sum of the boat's speed and the speed of the current. Therefore, the boat's speed is 3.6 km / (30 min / 60 min/h) = 7.2 km/h.

When traveling against the current, the effective speed of the boat is the difference between the boat's speed and the speed of the current. Therefore, the boat's speed is 3.6 km / (40 min / 60 min/h) = 5.4 km/h.

We can set up the following equations to solve for the speed of the current:

7.2 km/h = boat's speed + x km/h (equation 1)

5.4 km/h = boat's speed - x km/h (equation 2)

Solving these equations simultaneously will give us the speed of the current.

Calculation

Let's solve equations 1 and 2:

7.2 km/h = boat's speed + x km/h

5.4 km/h = boat's speed - x km/h

Adding the two equations together, we get:

12.6 km/h = 2 * boat's speed

Dividing both sides by 2, we find:

boat's speed = 6.3 km/h

Substituting this value back into equation 1, we can solve for the speed of the current:

6.3 km/h = boat's speed + x km/h

6.3 km/h = 6.3 km/h + x km/h

x km/h = 0 km/h

Therefore, the speed of the river's current is 0 km/h.

Time for Rafts to Cover the Same Distance

To determine the time it would take for rafts to cover the same distance, we need to know the speed at which the rafts can travel. Since the problem does not provide this information, we cannot calculate the time for rafts to cover the distance.

Conclusion

The speed of the river's current is 0 km/h. However, without knowing the speed at which the rafts can travel, we cannot determine the time it would take for rafts to cover the same distance.

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