Question

Сумма скорости катера по течению и скорости против течения равна 44 км /ч. Катер проплывает по течению за 5 ч такое же расстояние, какое он проплывает против течения за 6 ч. Найдите скорость катера по течению и скскорость против течения с помощью системы.

Answer 1

Х- скорость катера по течению
у- скорость катера против течения , из условия задачи имеем
5х =6у
{
х + у  =44    умножим второе уравнение на 5 и от первого уравнения отнимем второе
 5х - 6у = 0
-{
  5х +5у = 220   . получаем   - 6у -5у = - 220      -11у = -220       у =20 км/ч - скорость движения катера против течения
из второго уравнения получим скорость движения катера по течению х +у =44
х = 44 - у          х = 44 - 20      х = 24 км/ч

Answer 2

Problem Analysis

We are given that the sum of the speed of a boat in still water and the speed against the current is 44 km/h. The boat takes 5 hours to travel a certain distance with the current and 6 hours to travel the same distance against the current. We need to find the speed of the boat in still water and the speed of the current.

Solution

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

When the boat is traveling with the current, the effective speed is the sum of the boat's speed and the current's speed. So, the boat covers the distance in 5 hours: x + y = distance/5 ---(1)

When the boat is traveling against the current, the effective speed is the difference between the boat's speed and the current's speed. So, the boat covers the same distance in 6 hours: x - y = distance/6 ---(2)

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

Solving the Equations

To solve the equations, we can use the method of substitution or elimination. Let's use the method of substitution.

From equation (1), we can express distance in terms of x and y: distance = (x + y) * 5

Substituting this value of distance in equation (2), we get: (x - y) = [(x + y) * 5] / 6

Simplifying the equation: 6x - 6y = 5x + 5y

Rearranging the terms: x = 11y

Now, we can substitute this value of x in equation (1): 11y + y = distance/5

Simplifying the equation: 12y = distance/5

Rearranging the terms: distance = 60y

Now, we have two equations: 12y = distance/5 ---(3) distance = 60y ---(4)

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

Solving Equations (3) and (4)

To solve equations (3) and (4), we can substitute the value of distance from equation (4) into equation (3):

12y = (60y)/5

Simplifying the equation: 12y = 12y

This equation is true for any value of y. Therefore, we can choose any value for y.

Let's choose y = 1 for simplicity.

Substituting y = 1 in equation (4), we get: distance = 60 * 1 = 60 km

Now, we can substitute y = 1 and distance = 60 in equation (1) to find the value of x:

x + 1 = 60/5

Simplifying the equation: x + 1 = 12

Rearranging the terms: x = 11

Therefore, the speed of the boat in still water is 11 km/h and the speed of the current is 1 km/h.

Answer

The speed of the boat in still water is 11 km/h and the speed of the current is 1 km/h.