Question

теплоход прошел 100 километров по течению реки и 6 км против течения потратив на весь путь 9 часов Найдите скорость теплохода в стоячей воды если скорость течения равна 2 км/час​

Answer 1

v - скорость теплохода в стоячей воде

100/(v+2)+6/(v-2)=9

100v-200+6v+12=9*(v^2-4)

106v-188=9v^2-36;

9v^2-106v+152=0;

D=1441

v1=(53+sqrt(1441))/9≅10.11 км/ч

v2=(53-sqrt(1441))/9≅1.67 км/ч

Второй корень не имеет смысла, так как против течени теплоход плыть бы не смог (v2<2)
Ответ: v1≅10.11 км/ч

Answer 2

Ответ:

S(1)/(v+v(теч))+S(2)/(v-v(теч))=t

100/(v+2)+6/(v-2)=9

(100(v-2)+6(v+2))/(v²-2²)=9

(100v-200+6v+12)/(v²-4)=9

(106v-188)/(v²-4)=9

9(v²-4)=106v-188

9v²-36-106v+188=0

9v²-106v+152=0

v(1;2)=(106±√(106²-4*9*152))/18

v(1)=√(1441)/9+5+8/9≈10.10672286580051

v(2)= -√(1441)/9+5+8/9≈1.671054911977266

Answer 3

Calculation of the Speed of the Boat in Still Water

To find the speed of the boat in still water, we can use the concept of relative velocity. The speed of the boat in still water can be calculated by subtracting the speed of the river current from the boat's speed when traveling upstream or adding the speed of the river current to the boat's speed when traveling downstream.

Given the information provided: - The boat traveled 100 kilometers downstream (with the current) and 6 kilometers upstream (against the current). - The total time taken for the entire journey was 9 hours. - The speed of the river current is 2 kilometers per hour.

Let's assume the speed of the boat in still water is x kilometers per hour.

When the boat is traveling downstream, its effective speed is the sum of its speed in still water and the speed of the river current. Therefore, the time taken to travel downstream is given by the equation:

100 / (x + 2) = t1 (Equation 1)

When the boat is traveling upstream, its effective speed is the difference between its speed in still water and the speed of the river current. Therefore, the time taken to travel upstream is given by the equation:

6 / (x - 2) = t2 (Equation 2)

Since the total time taken for the entire journey is 9 hours, we can write the equation:

t1 + t2 = 9 (Equation 3)

Now, let's solve these equations to find the value of x, which represents the speed of the boat in still water.

From Equation 1, we can rewrite it as:

100 = t1 * (x + 2)

Similarly, from Equation 2, we can rewrite it as:

6 = t2 * (x - 2)

Substituting the values of t1 and t2 from Equation 3, we get:

100 = (9 - t2) * (x + 2) (Equation 4)

6 = t2 * (x - 2) (Equation 5)

Simplifying Equation 4, we have:

100 = 9x + 18 - 2t2x - 4t2

Simplifying Equation 5, we have:

6 = t2x - 2t2

Rearranging Equation 4, we get:

9x - 2t2x = 82 - 4t2 (Equation 6)

Substituting the value of t2 from Equation 5 into Equation 6, we have:

9x - 2(6 + 2x) = 82 - 4(6 + 2x)

Simplifying the equation further, we get:

9x - 12 - 4x = 82 - 24 - 8x

Combining like terms, we have:

5x - 12 = 58 - 8x

Simplifying further, we get:

13x = 70

Dividing both sides by 13, we find:

x = 70 / 13 ≈ 5.38

Therefore, the speed of the boat in still water is approximately 5.38 kilometers per hour.

Please note that the calculations are based on the information provided and the assumption that the boat's speed remains constant throughout the journey.