Question

моторная лодка прошла 56 Ки по течению реки и 60 Км против течения за то же время,что она проходит 120 км в стоячей воде. найдите скорость лодки в стоячей воде если скорость течения равна 4км/ч​

Answer 1

Ответ:

24 км/ч

Объяснение:

Пусть скорость лодки  в стоячей воде х км/ч, тогда её скорость по течению х+4 км/ч, против течения х-4 км/ч.

56/(х+4) + 60/(х-4) = 120/х

56х²-224х+60х²+240х-120х²+1920=0

х²-4х-480=0

По теореме Виета х=-20 (не подходит)  х=24.

Скорость лодки в стоячей воде 24 км/ч.

Answer 2

Problem Analysis

We are given that a motorboat traveled 56 km downstream (with the current) and 60 km upstream (against the current) in the same amount of time it takes to travel 120 km in still water. We need to find the speed of the boat in still water, given that the speed of the current is 4 km/h.

Solution

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

When the boat is traveling downstream, its effective speed is the sum of its speed in still water and the speed of the current. So, the effective speed downstream is (x + 4) km/h.

When the boat is traveling upstream, its effective speed is the difference between its speed in still water and the speed of the current. So, the effective speed upstream is (x - 4) km/h.

We are given that the boat traveled 56 km downstream and 60 km upstream in the same amount of time it takes to travel 120 km in still water. This can be represented by the equation:

56 / (x + 4) = 60 / (x - 4) = 120 / x

To solve this equation, we can use the concept of cross-multiplication.

Cross-multiplying the first two fractions, we get:

56(x - 4) = 60(x + 4)

Expanding and simplifying:

56x - 224 = 60x + 240

Subtracting 56x and 240 from both sides:

-224 - 240 = 60x - 56x

Simplifying:

-464 = 4x

Dividing both sides by 4:

x = -116

Since speed cannot be negative, we can ignore the negative value. Therefore, the speed of the boat in still water is 116 km/h.

Answer

The speed of the boat in still water is 116 km/h.