Question

Расстояние между двумя пристанями 80 км. Моторная лодка проходит это расстояние по течению реки за 4 ч, а против течения за 5 ч. Определите скорость течения реки?

Answer 1

Скорость лодки по течению  80 / 4 = 20 км/ч

Скорость лодки против течения  80 / 5 = 16 км/ч

Скорость течения  (20 - 16)/2 = 2 км/ч.

Answer 2

Problem Analysis

We are given that the distance between two ports is 80 km. A motorboat takes 4 hours to cover this distance with the current of the river and 5 hours to cover the same distance against the current. We need to determine the speed of the river's current.

Solution

Let's assume the speed of the motorboat in still water is x km/h, and the speed of the river's current is y km/h.

When the motorboat is moving with the current, its effective speed is the sum of its speed in still water and the speed of the current. Therefore, the effective speed is (x + y) km/h.

Similarly, when the motorboat is moving against the current, its effective speed is the difference between its speed in still water and the speed of the current. Therefore, the effective speed is (x - y) km/h.

We can use the formula distance = speed × time to create two equations based on the given information:

1. When moving with the current: 80 = (x + y) × 4 2. When moving against the current: 80 = (x - y) × 5

We can solve these equations simultaneously to find the values of x and y.

Solving the Equations

Let's solve the equations using the substitution method.

From equation 1, we can express x in terms of y: x = 80/4 - y = 20 - y (Equation 3)

Substituting this value of x into equation 2, we get: 80 = (20 - y - y) × 5 80 = (20 - 2y) × 5 80 = 100 - 10y 10y = 100 - 80 10y = 20 y = 20/10 y = 2 km/h

Substituting this value of y into equation 3, we can find x: x = 20 - 2 x = 18 km/h

Answer

Therefore, the speed of the river's current is 2 km/h.

Please note that the given search results did not provide specific information related to this problem. The solution was derived using mathematical equations and the given information.