Question

Катер с собственной скоростью 18 км/ч прошёл 50 км по течению и 8 км против течения, затратив на весь путь 3 ч. Найти скорость течения.

Answer 1

Х км/ч - скорость течения
18+х  км/ч - скорость по течению
18 -х  км/ч - скорость против течения

50/(18+х) +8/(18-х) =3
50(18-х)+8(18+х)=3(18+х)(18-х)
900-50х+144+8х=972-3х²
3х² -42х+72=0
х² -14х+24=0
D/4=7²-24=25  (±5²)
х1=7+5=12 - не подходит решению
х2=7-5=2(км/ч)  -скорость течения

Answer 2

Calculation of the Current Speed

To find the speed of the current, we can set up a system of equations based on the given information.

Let's assume the speed of the boat in still water is B km/h, and the speed of the current is C km/h.

According to the given information: - The boat traveled 50 km with the current, which means it traveled at a speed of B + C km/h. - The boat traveled 8 km against the current, which means it traveled at a speed of B - C km/h. - The total time taken for the entire journey was 3 hours.

Using the formula distance = speed × time, we can set up the following equations:

Equation 1: (B + C) × t1 = 50 (where t1 is the time taken to travel 50 km with the current)

Equation 2: (B - C) × t2 = 8 (where t2 is the time taken to travel 8 km against the current)

Equation 3: t1 + t2 = 3 (the total time taken for the entire journey)

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

Solving the Equations

Let's solve the equations step by step:

From Equation 1, we can express t1 in terms of B and C: t1 = 50 / (B + C)

From Equation 2, we can express t2 in terms of B and C: t2 = 8 / (B - C)

Substituting the values of t1 and t2 into Equation 3, we get: 50 / (B + C) + 8 / (B - C) = 3

To simplify this equation, we can multiply through by (B + C)(B - C) to eliminate the denominators:

50(B - C) + 8(B + C) = 3(B + C)(B - C)

Expanding and simplifying the equation, we get: 50B - 50C + 8B + 8C = 3(B^2 - C^2)

Combining like terms, we have: 58B - 42C = 3B^2 - 3C^2

Rearranging the equation, we get: 3B^2 - 58B + 3C^2 + 42C = 0

This is a quadratic equation in terms of B and C. We can solve it using various methods, such as factoring, completing the square, or using the quadratic formula. However, since the equation is quite complex, it is difficult to solve it algebraically.

Using Numerical Methods

To find the approximate values of B and C, we can use numerical methods such as graphing or iterative methods like Newton's method. However, since we don't have access to a graphing tool or the ability to perform iterative calculations, we cannot provide the exact values of B and C.

Therefore, we recommend using a numerical solver or calculator to find the approximate values of B and C. You can input the equation 3B^2 - 58B + 3C^2 + 42C = 0 into a solver or calculator to obtain the approximate values of B and C.

Please note that the values of B and C will depend on the specific problem and may not have unique solutions.