Question

Скорость лодки в стоячей воде равна 13 кмч. Валерий по течению проплыл 8 км и потратил на это столько времени, сколько плыл против течения 5 км. Вычислите скорость течения реки.

Answer 1

T1 = t2
S1= 8 км
S2= 5 км
Vстояч=13км/ч
Vтеч = ? км/ч
по формуле время :
$t= \frac{s}{v}$
Пусть x - скорость течения
$\frac{8}{13+x} = \frac{5}{13-x}$
$8*(13-x) = 5*(13+x)$
$104-8x=65 +5x$
$104-65=5x+8x$
$39=13x$
$x=39:13$
$x=3$(км/ч) скорость течения
Ответ : Скорость течения - 3 км/ч

Answer 2

Problem Analysis

We are given that the speed of a boat in still water is 13 km/h. Valeriy traveled 8 km downstream and spent the same amount of time traveling 5 km upstream. We need to calculate the speed of the river's current.

Solution

Let's assume the speed of the river's current is x km/h.

When Valeriy is traveling downstream, his effective speed is the sum of the speed of the boat in still water and the speed of the current. So, his effective speed is (13 + x) km/h.

When Valeriy is traveling upstream, his effective speed is the difference between the speed of the boat in still water and the speed of the current. So, his effective speed is (13 - x) km/h.

We are given that Valeriy spent the same amount of time traveling downstream for 8 km as he did traveling upstream for 5 km. This means that the time taken for both distances is equal.

We can use the formula time = distance / speed to set up an equation:

8 / (13 + x) = 5 / (13 - x)

To solve this equation, we can cross-multiply and simplify:

8(13 - x) = 5(13 + x)

Simplifying further:

104 - 8x = 65 + 5x

Combining like terms:

13x = 39

Dividing both sides by 13:

x = 3

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

Answer

The speed of the river's current is 3 km/h.