Question

Моторная лодка прошла против течения реки 72 км и вернулась в пункт отправления,затратив на обратный путь на 6 часов меньше.Найдите скорость течения, если скорость лодки в неподвижной воде 9 км/к.Ответ дайте в км/ч

Answer 1

Пусть х км/ч-скорость течения реки, тогда (9+х) км/ч - скорость лодки по течению реки, а (9-х) км/ч - скорость лодки против течения реки.
Составим уравнение 
72/(9-х)-72/(9+х)=6
Домножим уравнение на (9-х)(9+х), получим
72(9+х)-72(9-х)=6(9-х)(9+х)
72(9+х-9+х)=6(81-х²)
72*2х=6(81-х²)
24х=81-х²
х²+24х-81=0
D=576+324=900=30²
x₁=(-24+30)/2=3
x₂=-27 (не соответствует условию задачи)

Ответ: 3 км/ч

Answer 2

Calculating the Speed of the River Current

To find the speed of the river current, we can use the given information about the motorboat's journey. Let's denote the speed of the motorboat in still water as V (in km/h) and the speed of the river current as C (in km/h).

The motorboat traveled 72 km against the current and then returned to the starting point, spending 6 hours less on the return trip. We can use this information to set up an equation to solve for the speed of the river current.

Using the formula distance = speed × time, we can calculate the time taken for each leg of the journey.

The time taken to travel 72 km against the current is given by: \[ t_1 = \frac{72}{(V - C)} \]

The time taken to travel 72 km with the current is given by: \[ t_2 = \frac{72}{(V + C)} \]

Given that the return trip took 6 hours less, we have the equation: \[ t_1 - t_2 = 6 \]

Let's solve for the speed of the river current using the given equation.

Solving for the Speed of the River Current: \[ \frac{72}{(V - C)} - \frac{72}{(V + C)} = 6 \]

Using algebraic manipulation, we can solve for C: \[ 72 \times [(V + C) - (V - C)] = 6 \times (V + C)(V - C) \] \[ 72 = V^2 - C^2 \] \[ C^2 = V^2 - 72 \] \[ C = \sqrt{V^2 - 72} \]

Given that the speed of the motorboat in still water is 9 km/h, we can calculate the speed of the river current.

Calculating the Speed of the River Current: \[ C = \sqrt{9^2 - 72} \] \[ C = \sqrt{81 - 72} \] \[ C = \sqrt{9} \] \[ C = 3 \, \text{km/h} \]

Therefore, the speed of the river current is 3 km/h.

[[SOURCE #1]]