Question

Туристи пливли на байдарці 3 год за течією річки та 2 год проти течії. Шлях, який байдарка пропливла за течією, був на 16,5 км довшим, ніж шлях, пройдений проти течії. Знайдіть швидкість байдарки у км/год у стоячій воді, якщо швидкість течії дорівнює 1,7 км/год,

Answer 1

Ответ:

8 км/год.

Пошаговое объяснение:

Нехай швидкість байдарки у стоячій воді х км/год, тоді її швидкість за течією х+1,7 км/год, проти течії  х-1,7 км/год. Маємо рівняння:

3(х+1,7)-2(х-1,7)=16,5

3х+5,1-2х+3,4=16,5

х=8

Швидкість байдарки 8 км/год.

Answer 2

To find the speed of the kayak in still water, we can use the concept of relative velocity. Let's break down the information given:

- The tourists paddled downstream for 3 hours. - They paddled upstream for 2 hours. - The distance covered downstream was 16.5 km longer than the distance covered upstream. - The speed of the current is 1.7 km/h.

Calculating the Speed of the Kayak in Still Water:

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

When paddling downstream, 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 current. Therefore, the speed downstream is (x + 1.7) km/h.

When paddling upstream, 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 current. Therefore, the speed upstream is (x - 1.7) km/h.

We know that the time taken downstream is 3 hours and the time taken upstream is 2 hours. We can use the formula distance = speed × time to calculate the distances covered:

- Distance downstream = (x + 1.7) km/h × 3 hours - Distance upstream = (x - 1.7) km/h × 2 hours

According to the problem, the distance downstream is 16.5 km longer than the distance upstream. Therefore, we can set up the following equation:

(x + 1.7) × 3 = (x - 1.7) × 2 + 16.5

Now, let's solve this equation to find the value of x.

Solving the Equation:

Expanding the equation, we get:

3x + 5.1 = 2x - 3.4 + 16.5

Combining like terms, we have:

3x + 5.1 = 2x + 13.1

Subtracting 2x from both sides, we get:

x + 5.1 = 13.1

Subtracting 5.1 from both sides, we have:

x = 8

Therefore, the speed of the kayak in still water is 8 km/h.

Please note that the calculations are based on the information provided.