Question

помогите пожалуйста задачу!!!! ЗАДАЧА : Турист проплыл на байдарке 10 км против течения реки и 18 км по течению, затратив на весь путь сколько же времени, сколько ему понадобилось бы, чтобы проплыть по озеру 28 км, Зная, что скорость течения реки равна 2 км / ч, Найдите собственную скорость байдарки. зарание спасибо))))

Answer 1

t1=10:(Vb-Vr) -время в пути против течения (V бойдарки, V реки)

t2=18:(Vb+Vr)-время в пути по течению

t1+t2=10:(Vb-Vr)+18:(Vb+Vr)=28:Vb   - время пути по озеру

Vb=7км/ч

Answer 2

Пусть скорость байдарки х км/ч

Составим уравнение

10/(х-2)+18/(х+2)=28/х

10х(х+2)+18х(х-2)=28(х^2-4)

х=7

Скорость байдарки 7км/ч

 

Answer 3

Problem Analysis

To solve this problem, we need to find the time it took for the tourist to travel a total distance of 10 km against the current and 18 km with the current. We also need to find the time it would take for the tourist to travel 28 km on a lake, assuming the current speed is 2 km/h. Finally, we need to determine the speed of the kayak.

Solution

Let's start by finding the time it took for the tourist to travel 10 km against the current and 18 km with the current. We can use the formula `time = distance / speed` to calculate the time.

The time taken to travel 10 km against the current can be calculated as `time1 = 10 km / kayak_speed`.

The time taken to travel 18 km with the current can be calculated as `time2 = 18 km / (kayak_speed + current_speed)`.

Next, let's find the time it would take for the tourist to travel 28 km on the lake, assuming the current speed is 2 km/h. We can use the same formula `time = distance / speed`.

The time taken to travel 28 km on the lake can be calculated as `time3 = 28 km / kayak_speed`.

Now, we can set up an equation using the given information and solve for the kayak speed.

Since the time taken to travel 10 km against the current and the time taken to travel 18 km with the current are the same, we can equate `time1` and `time2`:

`10 km / kayak_speed = 18 km / (kayak_speed + 2 km/h)`.

Simplifying the equation, we get:

`10(kayak_speed + 2) = 18(kayak_speed)`.

Expanding and rearranging the equation, we get:

`10kayak_speed + 20 = 18kayak_speed`.

`8kayak_speed = 20`.

`kayak_speed = 20 / 8`.

`kayak_speed = 2.5 km/h`.

Therefore, the speed of the kayak is 2.5 km/h.

Answer

The speed of the kayak is 2.5 km/h.

Please let me know if you need any further assistance!