Question

Лодка может проплыть 15 км по течению реки и 6 еще км против течения за то же время, за какое плот может проплыть 5 км по этой реке. Найдите скорость течения реки, если известно, что собственная скорость лодки 8 км/ч.

Answer 1

2 км/ч х=(42-38)/2=2 и х=(42+38)/2=40

Answer 2

Problem Analysis

We are given that a boat can travel 15 km downstream (with the current) and 6 km upstream (against the current) in the same amount of time. We need to find the speed of the river current, given that the boat's own speed is 8 km/h.

Solution

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

When the boat is traveling downstream, its effective speed is the sum of its own speed and the speed of the current. Therefore, the boat's effective speed downstream is 8 + x km/h.

When the boat is traveling upstream, its effective speed is the difference between its own speed and the speed of the current. Therefore, the boat's effective speed upstream is 8 - x km/h.

We are given that the boat can travel 15 km downstream and 6 km upstream in the same amount of time. Let's denote the time taken for both distances as t.

Using the formula speed = distance / time, we can set up the following equations:

Downstream speed = Distance downstream / Time = 15 / t = 8 + x

Upstream speed = Distance upstream / Time = 6 / t = 8 - x

We can solve these two equations simultaneously to find the value of x.

Solution Steps

1. Set up the equations using the given information: - 15 / t = 8 + x - 6 / t = 8 - x 2. Solve the equations simultaneously to find the value of x. 3. Substitute the value of x back into one of the equations to find the value of t. 4. Provide the final answer for the speed of the river current.

Detailed Solution

Let's solve the equations to find the value of x:

Equation 1: 15 / t = 8 + x Equation 2: 6 / t = 8 - x To eliminate the variable t, we can multiply Equation 1 by 6 and Equation 2 by 15:

6 * (15 / t) = 6 * (8 + x)

15 * (6 / t) = 15 * (8 - x)

Simplifying the equations:

90 / t = 48 + 6x

90 / t = 120 - 15x

Now, we can set the two right-hand sides equal to each other:

48 + 6x = 120 - 15x

Adding 15x to both sides and subtracting 48 from both sides:

21x = 72

Dividing both sides by 21:

x = 72 / 21

Simplifying:

x ≈ 3.43 km/h

Now, let's substitute the value of x back into Equation 1 to find the value of t:

15 / t = 8 + 3.43

15 / t ≈ 11.43

Cross-multiplying:

15 ≈ 11.43t

Dividing both sides by 11.43:

t ≈ 1.31 hours

Therefore, the speed of the river current is approximately 3.43 km/h and the time taken to travel 5 km upstream is approximately 1.31 hours.

Answer

The speed of the river current is approximately 3.43 km/h.