Question

Скорость катера на 16 км больше скорости течения реки.катер за 2 часа проплыл 18 км по течению реки и 20 км против течен ия реки каковы скорости катера и течения реки

Answer 1

х - скорость течения реки

16+х (км/ч) - скорость катера

16+х+х=16+2х (км/ч) скорость катера по течению

16+х-х=16 (км/ч) - скорость катера против течения

Т.к. по течению катер прошел 18 км, а против течения - 20 км и на весь путь затрати 2 часа, составим ур-е:

18/(16+2х) + 20/16 = 2

9/(8+х) = 2-1,25

9=0,75*(8+х)

9=6+0,75х

0,75х=3

х= 3:0,75

х= 4 (км/ч) - скорость течения

16+4= 20 (км/ч) - скорость катера

Ответ: Скорость катера 20 км/ч

Answer 2

Calculation of Boat Speed and River Current Speed

To calculate the speed of the boat and the speed of the river current, we can use the given information that the boat traveled 18 km downstream (with the current) in 2 hours and 20 km upstream (against the current) in 2 hours.

Let's assume the speed of the river current is x km/h. According to the given information, the boat's speed downstream (with the current) would be x + 16 km/h and the boat's speed upstream (against the current) would be x - 16 km/h.

Calculation of Boat Speed Downstream

The boat traveled 18 km downstream in 2 hours. We can use the formula distance = speed × time to calculate the boat's speed downstream:

18 km = (x + 16 km/h) × 2 hours

Simplifying the equation:

36 km = 2x + 32 km/h

2x = 36 km - 32 km/h

2x = 4 km/h

x = 2 km/h

Therefore, the speed of the river current is 2 km/h.

Calculation of Boat Speed Upstream

The boat traveled 20 km upstream in 2 hours. Using the same formula, we can calculate the boat's speed upstream:

20 km = (x - 16 km/h) × 2 hours

Simplifying the equation:

40 km = 2x - 32 km/h

2x = 40 km + 32 km/h

2x = 72 km/h

x = 36 km/h

Therefore, the speed of the river current is 36 km/h.

Summary of Results

Based on the calculations, the speed of the boat is:

- Downstream (with the current): 2 km/h + 16 km/h = 18 km/h - Upstream (against the current): 36 km/h - 16 km/h = 20 km/h

And the speed of the river current is 2 km/h.

Please note that these calculations are based on the given information and assumptions made.