Question

ПОМОГИТЕ, ПОЖАЛУЙСТА, ДАЮ 100 БАЛЛОВ!!! За 3 год за течією і 1 год проти течiï рiчки моторний човен проходить 64 км. За 1 год за течiєю рiчки і 2 год в озерi цей самий човен проходить 47 км. Знайдіть власну швидкість човна i швидкість течii.​

Answer 1

Problem Analysis

We are given that a motorboat travels 64 km downstream in 3 hours and 47 km upstream in 3 hours. We need to find the speed of the boat and the speed of the current.

Downstream Speed Calculation

Let's assume the speed of the boat is B km/h and the speed of the current is C 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 speed downstream can be calculated as:

B + C = 64/3 km/h

Upstream Speed Calculation

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 speed upstream can be calculated as:

B - C = 47/3 km/h

Solving the Equations

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

B + C = 64/3 (Equation 1)

B - C = 47/3 (Equation 2)

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

Solution

Adding Equation 1 and Equation 2, we get:

2B = (64/3) + (47/3)

Simplifying, we have:

2B = 111/3

B = (111/3) / 2

B = 37/3

Therefore, the speed of the boat is 37/3 km/h.

Substituting the value of B into Equation 1, we can find the speed of the current:

(37/3) + C = 64/3

C = (64/3) - (37/3)

C = 27/3

Therefore, the speed of the current is 9 km/h.

Answer

The speed of the boat is 37/3 km/h and the speed of the current is 9 km/h.