Question

Лодка прошла 12 км по реке и 4 км против течения, потратив на весь путь 2 часа. какова собственная скорость лодки, если текущая скорость составляет 4 км/ч?

Answer 1

Ответ:

S                V                  tпр. течения    6км         х - 3 км/ч       6/(х-3) ч   по течению    12км       х +3 км/ч       12/(х+3) ч.Vтеч.= 3км/чV собств. = хкм/ч6/(х -3) + 12/(х+3) = 2| * (х-3)(х+3)6(х+3) + 12(х-3) = 2(х² -9)6х +18 +12х -36 = 2х² -182х² -18х =0х(2х -18) = 0х = 0 ( не подходит по условию задачи)2х -18 = 02х = 18х = 9(км/ч) - скорость лодки в стоячей воде

Объяснение:

Answer 2

Problem Analysis

We are given the following information: - The boat traveled 12 km downstream. - The boat traveled 4 km upstream against the current. - The total time taken for the entire journey was 2 hours. - The current speed is 4 km/h.

We need to find the boat's own speed.

Solution

Let's assume the boat's own speed is x km/h.

To calculate the time taken for the downstream journey, we can use the formula: Time = Distance / Speed

For the downstream journey, the distance is 12 km and the speed is the sum of the boat's own speed and the current speed (x + 4 km/h).

So, the time taken for the downstream journey is: Time_downstream = 12 km / (x + 4 km/h)

Similarly, for the upstream journey, the distance is 4 km and the speed is the difference between the boat's own speed and the current speed (x - 4 km/h).

So, the time taken for the upstream journey is: Time_upstream = 4 km / (x - 4 km/h)

The total time taken for the entire journey is given as 2 hours.

So, we can write the equation: Time_downstream + Time_upstream = 2 hours

Substituting the values, we get: 12 km / (x + 4 km/h) + 4 km / (x - 4 km/h) = 2 hours

To solve this equation, we can cross-multiply and simplify.

Calculation

Let's solve the equation to find the boat's own speed.

Cross-multiplying the equation, we get: 12 km * (x - 4 km/h) + 4 km * (x + 4 km/h) = 2 hours * (x + 4 km/h) * (x - 4 km/h)

Simplifying further: 12x - 48 km + 4x + 16 km = 2(x^2 - 16 km^2)

Combining like terms: 16x - 32 km = 2x^2 - 32 km^2

Rearranging the equation: 2x^2 - 16x = 0

Factoring out 2x: 2x(x - 8) = 0

Setting each factor equal to zero: 2x = 0 or x - 8 = 0

Solving for x, we get: x = 0 or x = 8

Since the boat's speed cannot be zero, the boat's own speed is 8 km/h.

Answer

The boat's own speed is 8 km/h.

Note: The calculation assumes that the boat's speed remains constant throughout the journey and that there are no other factors affecting the boat's speed.