Question

Турист проплыл на байдарке 25 км по озеру и 9 км против течения реки за столько же времени, за сколько он проплыл бы по течению той же реки 56 км. Найдите скорость байдарки в стоячй воде, если скорость течения реки равно 2 км/ч.

Answer 1

Скорость байдарки в стоячей воде -х км/час

Составляем уравнение:

25/х + 9/(х-2)=56/(Х+2)

или  25*(х-2)*(х+2) + 9*х*(х+2)=56*х*(х-2)

25(хх-4) + 9хх+18х=56хх-112х

22хх-130х+100=0

Решаем квадратное уравнение, откуда  х=5км/час

Проверка: 25/5+9/(5-2)=56/(5+2) или 5+3=56/7 8=8 

Answer 2

Problem Analysis

We are given the following information: - A tourist paddled a kayak for 25 km across a lake. - The tourist paddled against the current of a river for 9 km. - The time taken to paddle across the lake and against the current of the river is the same. - The speed of the river's current is 2 km/h.

We need to find the speed of the kayak in still water.

Solution

Let's assume the speed of the kayak in still water is x km/h.

When the tourist paddles across the lake, the speed of the kayak relative to the ground is the sum of the kayak's speed in still water and the speed of the river's current. Therefore, the speed of the kayak across the lake is (x + 2) km/h.

When the tourist paddles against the current of the river, the speed of the kayak relative to the ground is the difference between the kayak's speed in still water and the speed of the river's current. Therefore, the speed of the kayak against the current is (x - 2) km/h.

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

For the journey across the lake: - Distance = 25 km - Speed = (x + 2) km/h - Time = 25 / (x + 2) hours

For the journey against the current: - Distance = 9 km - Speed = (x - 2) km/h - Time = 9 / (x - 2) hours

Since the time taken for both legs of the journey is the same, we can set up the following equation:

25 / (x + 2) = 9 / (x - 2)

To solve this equation, we can cross-multiply:

25(x - 2) = 9(x + 2)

Simplifying the equation:

25x - 50 = 9x + 18

16x = 68

x = 68 / 16

x ≈ 4.25

Therefore, the speed of the kayak in still water is approximately 4.25 km/h.

Answer

The speed of the kayak in still water is approximately 4.25 km/h.