Question

Двигаясь по течению реки, расстояние в 72 км моторная лодка проходит за 3 ч., а плот — за 18 ч. Вычисли скорость моторной лодки при движении против течения реки.

Answer 1

Calculation of Speed of Motorboat Against the Current

To calculate the speed of the motorboat when moving against the current, we need to use the concept of relative velocity. The speed of the motorboat relative to the water is the difference between the speed of the motorboat in still water and the speed of the current.

Let's denote the speed of the motorboat in still water as x and the speed of the current as y.

Given that the motorboat covers a distance of 72 km in 3 hours when moving with the current, we can set up the following equation:

72 = (x + y) * 3 Similarly, when the motorboat moves against the current, it covers the same distance of 72 km in 18 hours. We can set up another equation:

72 = (x - y) * 18 To find the speed of the motorboat when moving against the current, we can solve these two equations simultaneously.

Let's start by rearranging the first equation to solve for y:

y = (72 / 3) - x

Substituting this value of y into the second equation, we get:

72 = (x - (72 / 3) + x) * 18

Simplifying the equation:

72 = (2x - 24) * 18

72 = 36x - 432

36x = 504

x = 14

Now that we have found the speed of the motorboat in still water (x), we can substitute this value back into the first equation to find the speed of the current (y):

72 = (14 + y) * 3

Simplifying the equation:

72 = 42 + 3y

3y = 30

y = 10

Therefore, the speed of the motorboat when moving against the current is 14 km/h.

Please note that the sources provided do not contain relevant information for this specific calculation.