Question

Моторний човен за течією річки пройшов 180 км / за 10 год , а зворотній шлях за 15 год . Знайдіть власну швидкість катера та швидкість течії ?

Answer 1

180/10=18км/ч скорость по течению

180/15=12км/ч против течения

(18-12)/2=3км/ч скорость течения

18-3=15км/ч скорость катера

Answer 2

I can help you with your math problem. Here is a detailed solution:

Let $v$ be the speed of the boat in still water and $u$ be the speed of the current. Then the speed of the boat downstream is $v+u$ and the speed of the boat upstream is $v-u$. The distance traveled in both directions is the same, 180 km. The time taken to go downstream is 10 hours and the time taken to go upstream is 15 hours. We can write two equations using these information:

$$ \begin{aligned} 180 &= (v+u) \times 10 \\ 180 &= (v-u) \times 15 \end{aligned} $$

To solve for $v$ and $u$, we can add the two equations and get:

$$ 360 = 25v $$

Dividing both sides by 25, we get:

$$ v = 14.4 $$

This means the speed of the boat in still water is 14.4 km/h. To find the speed of the current, we can substitute this value into either equation and get:

$$ \begin{aligned} 180 &= (14.4+u) \times 10 \\ u &= \frac{180-144}{10} \\ u &= 3.6 \end{aligned} $$

This means the speed of the current is 3.6 km/h.

Therefore, the speed of the boat in still water is 14.4 km/h and the speed of the current is 3.6 km/h.