Question

Моторная лодка прошла против течения реки 77 км и вернулась в пункт отправления, затратив на обратный путь на 2 часа меньше. Найдите скорость лодки в стоячей воде, если скорость течения равна 4км/ч. Ответ дайте в км/ч.

Answer 1

Х - скорость лодки в стоячей воде
х+4 - скорость по течению
х-4 - скорость против течения
77/(х-4) - время хода против течения
77/х+4) - время хода по течению
77/(х+4)+2=77(х-4)  (умножим на (х+4)(х-4))
77(х-4)+2(х+4)(х-4)=77(х+4)
77х-308+2(х2-4х+4х-16)=77х+308
-308+2х2-32=308
2х2=308+308+32
2х2=648  (сократим на 2)
х2=324
х"=-18 (не подходит по условию)
х=18 (км/ч)
Ответ: скорость лодки в стоячей воде 18 км/ч

PS: 2х2 - это 2х в квадрате

Answer 2

V-x
t-y
{(x-4)*y=77
{(x+4)*(y-2)=77
#2
77/(x+4)-77/(x-4)=2
#3
77/(x-4)-2=77/x+4

Answer 3

Problem Analysis

We are given that a motorboat traveled 77 km against the current of a river and then returned to the starting point, spending 2 hours less on the return journey. We need to find the speed of the boat in still water, given that the speed of the current is 4 km/h.

Solution

Let's assume the speed of the boat in still water is x km/h. Since the boat is traveling against the current, its effective speed will be (x - 4) km/h. On the return journey, the boat is traveling with the current, so its effective speed will be (x + 4) km/h.

We can use the formula distance = speed × time to calculate the time taken for each leg of the journey.

On the first leg of the journey (against the current), the boat traveled a distance of 77 km. The time taken for this leg can be calculated as:

77 = (x - 4) × t1 (Equation 1)

On the return journey (with the current), the boat traveled the same distance of 77 km, but this time it took 2 hours less. The time taken for this leg can be calculated as:

77 = (x + 4) × (t1 - 2) (Equation 2)

We can solve this system of equations to find the value of x, which represents the speed of the boat in still water.

Let's solve the equations:

From Equation 1, we can express t1 in terms of x:

t1 = 77 / (x - 4)

Substituting this value of t1 into Equation 2, we get:

77 = (x + 4) × (77 / (x - 4) - 2)

Simplifying this equation will give us the value of x.

Calculation

Let's calculate the value of x using the given equations.

77 = (x + 4) × (77 / (x - 4) - 2)

Simplifying the equation:

77 = (x + 4) × (77 - 2(x - 4))

77 = (x + 4) × (77 - 2x + 8)

77 = (x + 4) × (85 - 2x)

Expanding the equation:

77 = 85x + 340 - 2x^2 - 8x

0 = 2x^2 + 8x - 85x - 77 - 340

0 = 2x^2 - 77x - 417

Now, we can solve this quadratic equation to find the value of x.

Using the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

where a = 2, b = -77, and c = -417.

Substituting the values into the formula:

x = (-(-77) ± √((-77)^2 - 4 * 2 * (-417))) / (2 * 2)

Simplifying:

x = (77 ± √(5929 + 3348)) / 4

x = (77 ± √9277) / 4

Calculating the square root of 9277:

√9277 ≈ 96.25

Substituting this value into the equation:

x = (77 ± 96.25) / 4

Now, we can calculate the two possible values of x:

x1 = (77 + 96.25) / 4 ≈ 43.81

**x2 = (77 - 96.25)