Question

Катер прошел 10 км вверх по течению и 12 км вниз по течению, время в пути - 2 часа. Если скорость реки 3 км / ч, какова скорость моторной лодки?​

Answer 1

Ответ:

10×2=20, 12×2=24, 24+12=36, 36÷3=12км

Answer 2

Ответ:

12

Пошаговое объяснение:

Данные

Пусть скорость моторной лодки = x и x>0 ;

тогда скорость по течению = x+3 ;

тогда скорость против течения = x-3 ;

время затраченное по течению $\frac{10}{x+3}$ ;

время затраченное против течения $\frac{12}{x-3}$ ;

1) составим уравнение времени:

$\frac{10}{x+3}$ + $\frac{12}{x-3}$ = 2

2) найдем общий множитель и посчитаем числители:

$\frac{22x+24-2x^{2} }{(x+3)(x-3)} =0$ и запишем x $\neq$ ±3

3) возьмем числитель и поделим его на -2 и выстроим в формулу дискриминанта (ax2 + bx + c = 0) :

x2-11x-12=0

4) ищем дискриминант:

D=121-4*(-12)=169=$13^{2}$

5) найдем корни:

$x=\frac{11+-13}{2}$ x1=12 x2=-1 (не удовлетворяет)

Answer 3

Problem Analysis

We are given that a boat traveled 10 km upstream and 12 km downstream in a total time of 2 hours. The speed of the river is given as 3 km/h. We need to find the speed of the motorboat.

Solution

Let's assume the speed of the motorboat is x km/h.

When the boat is traveling upstream, its effective speed is reduced by the speed of the river. So the speed of the boat relative to the ground is (x - 3) km/h.

When the boat is traveling downstream, its effective speed is increased by the speed of the river. So the speed of the boat relative to the ground is (x + 3) km/h.

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

The time taken to travel 10 km upstream is given by: 10 km = (x - 3) km/h × t1 hours The time taken to travel 12 km downstream is given by: 12 km = (x + 3) km/h × t2 hours We are also given that the total time taken for the journey is 2 hours: t1 + t2 = 2 hours We can solve these equations to find the value of x, which represents the speed of the motorboat.

Calculation

Let's solve the equations to find the value of x.

From the equation 10 km = (x - 3) km/h × t1 hours, we can rearrange it to solve for t1: t1 = 10 km / (x - 3) km/h From the equation 12 km = (x + 3) km/h × t2 hours, we can rearrange it to solve for t2: t2 = 12 km / (x + 3) km/h Substituting the values of t1 and t2 into the equation t1 + t2 = 2 hours, we get: 10 km / (x - 3) km/h + 12 km / (x + 3) km/h = 2 hours To solve this equation, we can multiply both sides by (x - 3)(x + 3) to eliminate the denominators: 10(x + 3) + 12(x - 3) = 2(x - 3)(x + 3) Expanding and simplifying the equation: 10x + 30 + 12x - 36 = 2(x^2 - 9) 22x - 6 = 2x^2 - 18 2x^2 - 22x - 12 = 0

We can solve this quadratic equation using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a)

Plugging in the values of a, b, and c: x = (-(-22) ± √((-22)^2 - 4(2)(-12))) / (2(2)) x = (22 ± √(484 + 96)) / 4 x = (22 ± √580) / 4 x = (22 ± 2√145) / 4 x = (11 ± √145) / 2

Therefore, the speed of the motorboat can be either (11 + √145) / 2 km/h or (11 - √145) / 2 km/h.

Answer

The speed of the motorboat can be either (11 + √145) / 2 km/h or (11 - √145) / 2 km/h, depending on the direction of travel.