Question

Скорость течения реки относится к собственной скорости катера как 2:11.Найдите собственную скорость катера и скорость течения, если за 3 часа катер прошёл вниз по реке 78 км

Answer 1

78:3=26км/ч 
26:(2+11)=2км/ч 
2*2=4км/ч - скорость течения реки

наверное так будет)

или уравнением можно)

Вычисляем расстояние за 1 час: 
78 : 3 = 26 
Это значит, что общая скорость (катера и реки) = 26 км/ч. 
2. Отделяем скорость реки 
Берём каждую долю за Х, тогда скорость реки 2Х, а скорость катера = 11Х. 
2Х+11Х=26 км/ч 
13Х=26 км/ч 
Х = 2 км/ч. 
Тогда скорость реки = 2Х = 2*2 = 4 км/ч

Answer 2

Calculation of the Boat's Speed and River Current Speed

To find the boat's speed and the river current speed, we can use the given information that the ratio of the river current speed to the boat's speed is 2:11, and the boat traveled 78 km downstream in 3 hours.

Let's assume the boat's speed is x km/h and the river current speed is y km/h.

The boat's speed relative to the still water can be calculated as the sum of the boat's speed and the river current speed: (x + y) km/h.

According to the given ratio, we have the equation:

(y / (x + y)) = (2 / 11)

To find the boat's speed, we can rearrange the equation as follows:

y = (2 / 11) * (x + y)

Now, let's substitute the value of y in terms of x into the equation:

y = (2 / 11) * (x + y)

11y = 2x + 2y

9y = 2x

x = (9 / 2) * y

We also know that the boat traveled 78 km downstream in 3 hours. The formula for distance is speed multiplied by time:

Distance = Speed * Time

78 km = (x + y) km/h * 3 hours

Now, let's substitute the value of x in terms of y into the equation:

78 km = ((9 / 2) * y + y) km/h * 3 hours

78 km = (11 / 2) * y km/h * 3 hours

Simplifying the equation:

78 km = (33 / 2) * y km/h * 3 hours

78 km = (99 / 2) * y km

Now, let's solve for y:

y = (78 km * 2) / (99 * 3) km/h

y = 1.1818... km/h

Substituting the value of y back into the equation to find x:

x = (9 / 2) * 1.1818... km/h

x = 6.5454... km/h

Therefore, the boat's speed is approximately 6.55 km/h and the river current speed is approximately 1.18 km/h.

Please note that these values are approximate due to rounding.