Question

Лодка может проплыть расстояние между двумя селениями, стоящими на берегу реки, за 4 ч по течению реки и за 8 ч против течения. Скорость течения реки 2 км/ч. Найдите собственную скорость лодки и расстояние между селениями.

Answer 1

X ---собственная скорость лодки
4(x+2)=8(x-2)
4x+8=8x-16
8x-4x=8+16
4x=24
x=24:4
x=6км/ч собственная скорость лодки
(6+2)*4=8*4=32км расстояние между селениями

Answer 2

Problem Analysis

We are given that a boat can travel a certain distance between two villages on the banks of a river in 4 hours downstream and 8 hours upstream. The speed of the river's current is given as 2 km/h. We need to find the speed of the boat and the distance between the villages.

Solution

Let's assume the speed of the boat is x km/h and the distance between the villages is d km.

When the boat is traveling downstream, its effective speed is the sum of its own speed and the speed of the river's current. So, the boat's effective speed downstream is (x + 2) km/h.

When the boat is traveling upstream, its effective speed is the difference between its own speed and the speed of the river's current. So, the boat's effective speed upstream is (x - 2) km/h.

We can use the formula speed = distance / time to calculate the speed, distance, and time for both scenarios.

Downstream Calculation

When the boat is traveling downstream, the time taken is 4 hours and the effective speed is (x + 2) km/h. Using the formula speed = distance / time, we can write the equation:

(x + 2) = d / 4

Upstream Calculation

When the boat is traveling upstream, the time taken is 8 hours and the effective speed is (x - 2) km/h. Using the formula speed = distance / time, we can write the equation:

(x - 2) = d / 8

Solving the Equations

We have two equations with two unknowns (x and d). We can solve these equations simultaneously to find the values of x and d.

Let's solve the equations:

From equation we have (x + 2) = d / 4. Rearranging, we get d = 4(x + 2).

Substituting this value of d in equation we get (x - 2) = (4(x + 2)) / 8.

Simplifying the equation, we get 8(x - 2) = 4(x + 2).

Expanding and simplifying further, we get 8x - 16 = 4x + 8.

Bringing the x terms to one side and the constant terms to the other side, we get 8x - 4x = 8 + 16.

Simplifying, we get 4x = 24.

Dividing both sides by 4, we get x = 6.

Now that we have the value of x, we can substitute it back into one of the equations to find the value of d.

Using equation we have (6 + 2) = d / 4.

Simplifying, we get 8 = d / 4.

Multiplying both sides by 4, we get 32 = d.

Answer

Therefore, the speed of the boat is 6 km/h and the distance between the villages is 32 km.