Question

Власна швидкість човна дорівнює 18км/год. Шлях у 20км за течією річки, човен пропливає на 15хв швидше, ніж проти течії. Знайдіть швидкість течії річки.

Answer 1

Пусть х км/час - скорость течения реки (0<x<18)
(18+x) км/час скорость лодки по течению реки
(18-x) км/час скорость лодки против течения реки
15 мин=15/60 часа=1/4 часа
$\frac{20}{18+x}$ часов время движения лодки по течению реки
$\frac{20}{18-x}$ часов время движения лодки против течения

уравнение:

$\frac{20}{x-18}- \frac{20}{x+18} = \frac{1}{4}$
ОДЗ:
$\left \{ {{18-x \neq 0} \atop {18+x \neq 0}} \right. , \left \{ {{x \neq 18} \atop {x \neq -18}} \right.$
=>  x≠18
$\frac{20*(18+x)-20*(18-x)}{ 18^{2}- x^{2} }= \frac{1}{4}$
$\frac{160x}{ 18^{2}- x^{2} } = \frac{1}{4}$
x²+160x-324=0
x₁=2, x₂=-162

x₂=-162 посторонний корень

ответ: скорость течения реки 2 км/час

Answer 2

Calculation of River Current Speed

To find the speed of the river current, we can use the given information about the boat's speed and the time it takes to travel a certain distance with and against the current.

Let's break down the problem:

- Boat's speed: 18 km/h - Distance traveled with the current: 20 km - Time taken to travel 20 km with the current: 15 minutes faster than against the current

To solve this problem, we can use the formula:

Speed = Distance / Time

Let's calculate the time taken to travel 20 km with the current:

Time with current = Time against current - 15 minutes

Since the time is given in minutes, we need to convert it to hours:

Time with current = (Time against current - 15) / 60 hours

Now, we can calculate the speed of the river current:

Speed of current = (Distance with current - Distance against current) / Time with current

Substituting the given values:

Speed of current = (20 km - 20 km) / [(Time against current - 15) / 60]

Now, let's calculate the speed of the river current using the given information.

According to the search result snippet from Source the calculation is not visible. However, we can still proceed with the calculation using the given information.

Let's assume the time taken to travel 20 km against the current is 't' hours.

Time against current = t hours

Using the formula mentioned above, we can calculate the speed of the river current:

Speed of current = (20 km - 20 km) / [(t - 15) / 60]

Simplifying the equation:

Speed of current = 0 km / [(t - 15) / 60]

Since the numerator is zero, the speed of the river current is 0 km/h.

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

Please note that the calculation assumes a constant speed of the river current throughout the entire journey.