Question

No1 Лодка плыла по течению реки 3 ч, а против течения - 4 ч. Путь, КОТОРЫЙ лодка прошла по течению оказался на 5 км больше, чем путь, который она проплыла против течения. Найдите скорость лодки в озере, если скорость течения реки равна 2 км/ч. 1) Заполните таблицу​

Answer 1

Ответ:

Пусть х км/ч -скорость лодки в озере ,

тогда (х+2) км/ч - скорость по течению,

. (х-2) км/ч - скорость против течения

. 3(х+2) км - путь лодки по течению

. 4(х-2)) км - путь лодки против течения

Известно,что путь по течению больше,чем путь против течения на 5 км

составим уравнение:

3(х+2) -4(х-2)=5

3х+6-4х+8=5

-х = -9

х=9 км/ч - скорость лодки по озеру

Ответ: 9 км/ч - скорость лодки по озеру

Answer 2

To solve this problem, let's start by filling in the table with the given information:

| | Distance (km) | Time (h) | |--------------|---------------|----------| | With current | | 3 | | Against current | | 4 |

We are given that the boat took 3 hours to travel with the current and 4 hours to travel against the current. Let's denote the speed of the boat in still water as "b" and the speed of the current as "c".

To find the distance traveled with the current, we can use the formula: Distance = Speed * Time.

For the boat traveling with the current, the speed of the boat is the sum of its own speed and the speed of the current, so the distance traveled with the current is (b + c) * 3.

For the boat traveling against the current, the speed of the boat is the difference between its own speed and the speed of the current, so the distance traveled against the current is (b - c) * 4.

We are also given that the distance traveled with the current is 5 km more than the distance traveled against the current. So we can write the equation:

(b + c) * 3 = (b - c) * 4 + 5

Now let's solve this equation to find the speed of the boat in still water.

Expanding the equation, we get:

3b + 3c = 4b - 4c + 5

Rearranging the terms, we get:

4c + 4b - 3b + 3c = 5

Simplifying, we get:

b + 7c = 5

To solve for b, we need another equation. We can use the fact that the speed of the current is given as 2 km/h. So we can write another equation:

b - c = 2

Now we have a system of two equations:

b + 7c = 5 b - c = 2

We can solve this system of equations using substitution or elimination method. I will use the substitution method.

From the second equation, we can isolate b:

b = c + 2

Substituting this value of b into the first equation, we get:

(c + 2) + 7c = 5

Combining like terms, we get:

8c + 2 = 5

Subtracting 2 from both sides, we get:

8c = 3

Dividing both sides by 8, we get:

c = 3/8

Now that we have the value of c, we can substitute it back into the second equation to find b:

b - (3/8) = 2

Adding (3/8) to both sides, we get:

b = 2 + (3/8)

Simplifying, we get:

b = 19/8

So the speed of the boat in still water is 19/8 km/h.

Therefore, the answer is: The speed of the boat in the lake is 19/8 km/h.