Question

От пристани A к пристани B, расстояние до которой равно 28,8 км, отправился плот. Через 0,4 ч навстречу ему от пристани B вышел катер, собственная скорость которого равна 17,5 км/ч, и встретился с плотом через 1,6 ч. Найдите скорость течения реки. ОЧЕНЬ СРОЧНО!!!!! ПОМОГИТЕ ПОЖАЛУЙСТА!!!!!!!!!!!

Answer 1

1,6 час+0,4 час=2 часа плыл плот до встречи с катером
х - скорость течения
S=Vt
2х - проплыл плот до встречи
1,6(17,5-х) - прошел катер до встречи (он шел против течения)
2х + 1,6(17,5-х) = 28,8
2х+28-1,6х=28,8
0,4х=28,8-28
0,4х=0,8
х=0,8:0,4
х=2 (км/час) - скорость течения
Ответ: скорость течения реки равна 2 км/час

Answer 2

Problem Analysis

We are given the following information: - The distance between port A and port B is 28.8 km. - A raft started from port A and traveled towards port B. - After 0.4 hours, a motorboat with a speed of 17.5 km/h started from port B and met the raft after 1.6 hours.

We need to find the speed of the river current.

Solution

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

The speed of the raft relative to the river current is the difference between the speed of the raft and the speed of the river current. Similarly, the speed of the motorboat relative to the river current is the difference between the speed of the motorboat and the speed of the river current.

We can set up the following equation based on the given information:

Distance traveled by the raft = Distance traveled by the motorboat

Let's calculate the distances traveled by the raft and the motorboat.

The distance traveled by the raft can be calculated as the product of the time taken (0.4 hours) and the speed of the raft relative to the river current (which is the speed of the raft minus the speed of the river current).

The distance traveled by the motorboat can be calculated as the product of the time taken (1.6 hours) and the speed of the motorboat relative to the river current (which is the speed of the motorboat minus the speed of the river current).

Setting up the equation:

Distance traveled by the raft = Distance traveled by the motorboat

(0.4 hours) * (speed of the raft - speed of the river current) = (1.6 hours) * (speed of the motorboat - speed of the river current)

Now, let's substitute the given values into the equation and solve for the speed of the river current.

Calculation

Given: - Distance between port A and port B = 28.8 km - Time taken by the raft = 0.4 hours - Time taken by the motorboat = 1.6 hours - Speed of the motorboat = 17.5 km/h

Let's assume the speed of the raft is r km/h.

The distance traveled by the raft = (0.4 hours) * (speed of the raft - speed of the river current)

The distance traveled by the motorboat = (1.6 hours) * (speed of the motorboat - speed of the river current)

Setting up the equation:

(0.4) * (r - x) = (1.6) * (17.5 - x)

Simplifying the equation:

0.4r - 0.4x = 28 - 1.6x

0.4r = 28 + 1.2x

0.4r - 1.2x = 28

Let's solve this equation to find the value of x.

Solution

To solve the equation 0.4r - 1.2x = 28, we need another equation. We can use the fact that the distance between port A and port B is 28.8 km.

The distance traveled by the raft = (0.4 hours) * (speed of the raft - speed of the river current)

Substituting the given values:

(0.4) * (r - x) = 28.8

0.4r - 0.4x = 28.8

Now we have a system of two equations:

0.4r - 1.2x = 28

0.4r - 0.4x = 28.8

We can solve this system of equations to find the values of r and x.

Let's solve the system of equations using the substitution method.

From the second equation, we can express r in terms of x:

0.4r = 0.4x + 28.8

r = x + 72

Substituting this value of r into the first equation:

0.4(x + 72) - 1.2x = 28

0.4x + 28.8 - 1.2x = 28

-0.8x = -0.8

x = 1

Therefore, the speed of the river current is 1 km/h.

Answer

The speed of the river current is 1 km/h.