Question

Катер прошел 80км по течению реки и вернулся обратно затратив на весь путь 9 ч. а)Найдите собственную скорость катера если скорость течения реки 2км/ч б)найдите скорость течения реки если скорость катера в стоячей воде 18км/ч

Answer 1

a) Пусть собст скорость - х, тогда скорость по теч. равно х+2, против равно х-2

Уравнение:$\frac{80}{x+2}+\frac{80}{x-2}=9\\ \frac{80x-160+80x+160}{x^{2}-4}=9\\ 9x^{2}-36-160x=0$

Решаем и получаем х=18. Ответ 18 км/ч

б)Учитывая предыдущий ответ, где скорость катера 18 км/ч, а скорость течения реки 2 км/ч,тут если скорость катера в стоячей воде 18 км/ч, то скорость течения реки будет 2км/ч

Answer 2

Calculation of the Boat's Speed and River Current Speed

To find the boat's speed and the speed of the river current, we can use the information provided in the question. Let's solve it step by step:

a) To find the boat's speed, we need to calculate the speed of the boat in still water. We can use the formula:

Boat's speed in still water = (Total distance traveled) / (Total time taken)

The boat traveled a total distance of 80 km upstream and 80 km downstream, which gives a total distance of 160 km. The total time taken for the entire journey is 9 hours.

Using the formula, we can calculate the boat's speed in still water:

Boat's speed in still water = 160 km / 9 hours

Now, let's calculate the boat's speed in still water:

Boat's speed in still water = 17.78 km/h b) To find the speed of the river current, we can use the formula:

Speed of the river current = (Boat's speed in still water - Boat's speed in flowing water) / 2

We already know the boat's speed in still water, which is 17.78 km/h. We need to find the boat's speed in flowing water.

The boat's speed in flowing water can be calculated by subtracting the speed of the river current from the boat's speed in still water. In this case, the speed of the river current is given as 2 km/h.

Boat's speed in flowing water = Boat's speed in still water - Speed of the river current

Boat's speed in flowing water = 17.78 km/h - 2 km/h

Now, let's calculate the boat's speed in flowing water:

Boat's speed in flowing water = 15.78 km/h

Finally, we can calculate the speed of the river current using the formula mentioned earlier:

Speed of the river current = (Boat's speed in still water - Boat's speed in flowing water) / 2

Speed of the river current = (17.78 km/h - 15.78 km/h) / 2

Now, let's calculate the speed of the river current:

Speed of the river current = 1 km/h Therefore, the boat's speed in still water is 17.78 km/h and the speed of the river current is 1 km/h.

Please note that these calculations are based on the information provided in the question and may not reflect real-world scenarios.