Question

Найдите скорость движения катера в стоячей воде ,если он прошел расстояние между двумя пристанями по течению реки за 2 часа,а против течения -за 3 часа.Скорость течения реки 2 км/ч.

Answer 1

Пусть скорость катера будет х км/ч, расстояние между пристанями будет 1 км.
Тогда скорость катера по течению реки (х+2) км/ч, против течения (х-2) км/ч
Составим уравнение 1/(x-2)-1/(x+2)=3-2
1/(x-2)-1/(x+2)=1 Умножим все уравнение на (х-2)(х+2)
(X+2)-(x-2)=x²-4
x+2-x+2=x²-4
x²-8=0
x=√8=2√2 км/ч

Answer 2

2( х + 2 ) = 3( х - 2 )
2х + 4 = 3х - 6
3х -2х = 4 + 6
х = 10 ( км/час )
Ответ 10 км/час

Answer 3

Calculating the Boat's Speed in Still Water

To calculate the speed of the boat in still water, we can use the formula: Boat's speed in still water = (Speed downstream + Speed upstream) / 2

First, let's calculate the speed of the boat downstream and upstream using the given information.

Speed Downstream

The boat traveled the distance between the two piers downstream in 2 hours. The speed of the river's current is 2 km/h.

The speed downstream can be calculated using the formula: Speed downstream = (Distance / Time) + Speed of the river's current

Substituting the given values: Speed downstream = (Distance / Time) + Speed of the river's current = (Distance / 2) + 2

Speed Upstream

The boat traveled the same distance between the two piers upstream in 3 hours.

The speed upstream can be calculated using the same formula: Speed upstream = (Distance / Time) - Speed of the river's current

Substituting the given values: Speed upstream = (Distance / 3) - 2

Now, we can calculate the boat's speed in still water using the formula mentioned earlier.

Boat's Speed in Still Water

Boat's speed in still water = (Speed downstream + Speed upstream) / 2

Substitute the calculated values: Boat's speed in still water = ((Distance / 2) + 2 + (Distance / 3) - 2) / 2

Let's calculate the boat's speed in still water using the given information and the formulas.

Calculating the Boat's Speed in Still Water

Using the given information and the formulas, the boat's speed in still water can be calculated as follows:

Speed downstream = (Distance / 2) + 2 Speed upstream = (Distance / 3) - 2 Boat's speed in still water = ((Distance / 2) + 2 + (Distance / 3) - 2) / 2

After calculating the boat's speed in still water, we can provide the final answer.