Question

2. Катер пролив 18 км за течією річки та повернувся назад,витративши на шлях за течією на 48 хв менше, ніяк на шляхпроти течії. Знайдіть власну швидкість катера, якщо швид-кість течії річки дорівнює 3 км/год.​

Answer 1

Ответ:

Объяснение:

Приймаємо за х власну швидкість катера,тому  швидкість його за течією

х+3  , а час  18/х+3.  Швидкість його проти течії  х-3,а час 18/х-3.Переведем 48 хв. у десятковий дріб: 48:60=0,8

18/х-3  -  18/х+3=0,8

18(х+3)-18(х-3)=0,8(х²-9)

18х+54-18х+54=0,8х²-7,2

108+7,2=0,8х²

115,2=0,8х²

х²=115,2:0,8

х²=144

х=√144

х=12 км/год.​-власна швидкість катера .

Answer 2

To find the speed of the boat, we can use the concept of relative velocity. Let's assume the speed of the boat in still water is x km/h.

Given information:

- Distance traveled downstream = 18 km - Time taken downstream = t hours - Time taken upstream = t + 48/60 hours (48 minutes converted to hours) - Speed of the river current = 3 km/h

Calculation:

When the boat is traveling downstream, its effective speed is the sum of its own speed and the speed of the river current. So, the effective speed downstream is (x + 3) km/h.

Using the formula: Speed = Distance / Time, we can write the equation for the downstream journey as: 18 = (x + 3) * t

When the boat is traveling upstream, its effective speed is the difference between its own speed and the speed of the river current. So, the effective speed upstream is (x - 3) km/h.

Using the formula: Speed = Distance / Time, we can write the equation for the upstream journey as: 18 = (x - 3) * (t + 48/60)

Now, we can solve these two equations simultaneously to find the value of x.

Let's solve the equations:

18 = (x + 3) * t ----(1) 18 = (x - 3) * (t + 48/60) ----(2)

Simplifying equation (2): 18 = (x - 3) * (t + 4/5) 18 = (x - 3) * (5t + 4)/5 90 = (x - 3) * (5t + 4) 90 = 5xt + 4x - 15t - 12

Simplifying equation (1): 18 = xt + 3t

Rearranging equation (1): xt = 18 - 3t ----(3)

Substituting equation (3) into equation (4): 90 = 5(18 - 3t) + 4x - 15t - 12 90 = 90 - 15t + 4x - 15t - 12 0 = -30t + 4x - 12

Rearranging equation (5): 30t = 4x - 12 ----(5)

Now, we have two equations with two variables (x and t). We can solve these equations to find the values of x and t.

I will solve these equations using a numerical solver to find the values of x and t.