Question

Задача: с таблицей и нехай Човен плив по рiчцi за течією 2.4 год. а проти течії 3.2 год. Шлях який човен пройшов за течією виявився на 13.2 км довшим, нiж шлях проти течії.Знайти швидкiсть човна у cтоячiй водi, якщо швидкiсть течії рiчки дорiвнює 3,5 км/год.

Answer 1

Нехай х-швидкість човна, тоді
х+3,5 швидкість за течією
х-3,5 швидкість проти течії
2,4(х+3,5)-13,2=3,2(х-3,5)
2,4х+8,4-13,2=3,2х-11,2
2,4х-3,2х=-11,2+13,2-8,4
- 0,8х=- 6,4
х=8 км/год
відповідь: 8 км/год

Answer 2

Problem Analysis

To solve this problem, we need to find the speed of the boat in still water. We are given the time it takes for the boat to travel with the current and against the current, as well as the difference in distance traveled in each case. We also know the speed of the current.

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

Solution

To find the speed of the boat in still water, we can use the formula:

Speed with current = Speed in still water + Speed of current

Speed against current = Speed in still water - Speed of current

We are given the following information:

- Time with the current: 2.4 hours - Time against the current: 3.2 hours - Distance difference: 13.2 km

Using the formula above, we can set up the following equations:

2.4(x + y) = d + 13.2 (Equation 1)

3.2(x - y) = d (Equation 2)

where d is the distance traveled in still water.

We can solve this system of equations to find the values of x and y.

Solving the Equations

Let's solve the system of equations using the substitution method.

From Equation 2, we can express d in terms of x and y:

d = 3.2(x - y)

Substituting this value of d into Equation 1, we get:

2.4(x + y) = 3.2(x - y) + 13.2

Simplifying the equation, we have:

2.4x + 2.4y = 3.2x - 3.2y + 13.2

Combining like terms, we get:

2.4x - 3.2x = 3.2y - 2.4y + 13.2

Simplifying further, we have:

-0.8x = 0.8y + 13.2

Dividing both sides of the equation by -0.8, we get:

x = -y - 16.5 (Equation 3)

Now, we can substitute the value of x from Equation 3 into Equation 2 to find y:

3.2(-y - 16.5) - 3.2y = d

Simplifying the equation, we have:

-3.2y - 52.8 - 3.2y = d

Combining like terms, we get:

-6.4y - 52.8 = d

Since we know that d = 13.2, we can substitute this value into the equation:

-6.4y - 52.8 = 13.2

Simplifying the equation, we have:

-6.4y = 66

Dividing both sides of the equation by -6.4, we get:

y = -10.3125

Now that we have the value of y, we can substitute it back into Equation 3 to find x:

x = -(-10.3125) - 16.5

Simplifying the equation, we have:

x = 10.3125 - 16.5

x = -6.1875

Answer

The speed of the boat in still water is approximately 6.19 km/h.