Question

моторная лодка за 2 часа проходит по течению реки 60 км а за 3 часа против течения 50 км. Определите скорость движения реки

Answer 1

Problem Analysis

We are given that a motorboat travels 60 km in 2 hours downstream and 50 km in 3 hours upstream. We need to determine the speed of the river's current.

Downstream Speed Calculation

Let's assume the speed of the motorboat in still water is B km/h, and the speed of the river's current is C km/h. When the motorboat is traveling downstream, the effective speed is the sum of the motorboat's speed and the speed of the current. Therefore, the downstream speed is B + C km/h.

According to the given information, the motorboat travels 60 km downstream in 2 hours. Using the formula distance = speed × time, we can write the equation:

60 = (B + C) × 2

Simplifying the equation, we get:

2B + 2C = 60

Upstream Speed Calculation

When the motorboat is traveling upstream against the current, the effective speed is the difference between the motorboat's speed and the speed of the current. Therefore, the upstream speed is B - C km/h.

According to the given information, the motorboat travels 50 km upstream in 3 hours. Using the formula distance = speed × time, we can write the equation:

50 = (B - C) × 3

Simplifying the equation, we get:

3B - 3C = 50

Solving the Equations

We now have a system of two equations with two variables:

Equation 1: 2B + 2C = 60

Equation 2: 3B - 3C = 50

We can solve this system of equations to find the values of B and C.

Solution

To solve the system of equations, we can use the method of substitution or elimination. Let's use the method of elimination to eliminate the variable C.

Multiplying Equation 1 by 3 and Equation 2 by 2, we get:

Equation 3: 6B + 6C = 180

Equation 4: 6B - 6C = 100

Adding Equation 3 and Equation 4, we eliminate the variable C:

12B = 280

Dividing both sides of the equation by 12, we find:

B = 23.33

Now, we can substitute the value of B into Equation 1 to find the value of C:

2(23.33) + 2C = 60

Simplifying the equation, we get:

46.66 + 2C = 60

Subtracting 46.66 from both sides of the equation, we find:

2C = 13.34

Dividing both sides of the equation by 2, we get:

C = 6.67

Answer

The speed of the motorboat in still water is approximately 23.33 km/h, and the speed of the river's current is approximately 6.67 km/h.