Question

В 6 часов утра лодка отправилась из пункта A в пункт B вниз по течению реки. Три часа спустя после прибытия в пункт B лодка отправилась в обратный путь и прибыла в A в 7 часов вечера того же дня. Найдите скорость течения реки, если собственная скорость лодки равна 5 км/ч, а расстояние между пунктами A и B составляет 24 км.

Answer 1

пусь скорости равна  х по течениб тогда  5+х , против 5-х

всего    была в пути   6+7=13  часов    3    часа        простояла  значит   13-3=10

24/(5+x)+24/(5-x)=10

24(5-x)+24(5+x)=10(25-x^2)

2*24*5=250-10x^2

10x^2=10

x=-/+1

Ответ  1 км/час

 

 

 

 

 

Answer 2

Решение Вашего задания во вложении

Answer 3

Problem Analysis

We are given the following information: - A boat departs from point A to point B downstream at 6:00 AM. - Three hours after arriving at point B, the boat returns to point A. - The boat arrives at point A at 7:00 PM on the same day. - The boat's own speed is 5 km/h. - The distance between points A and B is 24 km.

We need to find the speed of the river's current.

Solution

Let's assume the speed of the river's current is x km/h.

When the boat is traveling downstream from A to B, it benefits from the speed of the current, so its effective speed is the sum of its own speed and the speed of the current. Therefore, the boat's effective speed downstream is 5 + x km/h.

When the boat is traveling upstream from B to A, it has to overcome the speed of the current, so its effective speed is the difference between its own speed and the speed of the current. Therefore, the boat's effective speed upstream is 5 - x km/h.

We can use the formula speed = distance / time to calculate the time taken for each leg of the journey.

Let's calculate the time taken for the downstream journey first. The distance between A and B is 24 km, and the effective speed downstream is 5 + x km/h. Therefore, the time taken for the downstream journey is:

time downstream = distance / speed downstream = 24 / (5 + x)

Next, let's calculate the time taken for the upstream journey. The distance between B and A is also 24 km, and the effective speed upstream is 5 - x km/h. Therefore, the time taken for the upstream journey is:

time upstream = distance / speed upstream = 24 / (5 - x)

According to the given information, the total time for the entire journey is 13 hours (from 6:00 AM to 7:00 PM). Therefore, the sum of the time taken for the downstream and upstream journeys should be equal to 13 hours:

time downstream + time upstream = 13

Substituting the expressions for time downstream and time upstream, we get:

24 / (5 + x) + 24 / (5 - x) = 13

Now we can solve this equation to find the value of x, which represents the speed of the river's current.

Calculation

Let's solve the equation 24 / (5 + x) + 24 / (5 - x) = 13 to find the value of x.

To solve this equation, we can multiply both sides by the denominators to eliminate the fractions:

24(5 - x) + 24(5 + x) = 13(5 + x)(5 - x)

Simplifying the equation:

120 - 24x + 120 + 24x = 13(25 - x^2)

Combining like terms:

240 = 325 - 13x^2

Rearranging the equation:

13x^2 = 325 - 240

13x^2 = 85

Dividing both sides by 13:

x^2 = 85 / 13

Taking the square root of both sides:

x = sqrt(85 / 13)

Evaluating the square root:

x ≈ 2.56

Therefore, the speed of the river's current is approximately 2.56 km/h.

Answer

The speed of the river's current is approximately 2.56 km/h.