Question

баржа прошла против течения реки 240 км и, повернув обратно, прошла еще 180 км, затратив на весь путь 18 часов. найдите собственную скорость баржи, если скорость течения реки равна 5 км/ч

Answer 1

Ответ:

25

Объяснение:

x - собственная скорость баржи, км/ч.

240/(x-5) +180/(x+5)=18                         |6

(40(x+5)+30(x-5))/((x-5)(x+5))=3

40x+200+30x-150=3(x²-25)

3x²-75-70x-50=0

3x²-70x-125=0; D=4900+1500=6400

x₁=(70-80)/6=-10/6=-5/3 - ответ не подходит по смыслу.

x₂=(70+80)/6=150/6=25 км/ч

Answer 2

Problem Analysis

We are given that a barge traveled 240 km against the current of a river and then turned back and traveled an additional 180 km. The total time taken for the entire journey was 18 hours. We need to find the speed of the barge if the speed of the river current is 5 km/h.

Solution

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

When the barge is traveling against the current, its effective speed is reduced by the speed of the current. So, the speed of the barge relative to the ground is (x - 5) km/h.

When the barge is traveling with the current, its effective speed is increased by the speed of the current. So, the speed of the barge relative to the ground is (x + 5) km/h.

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

For the first leg of the journey (against the current), the distance is 240 km and the speed is (x - 5) km/h. So, the time taken is 240 / (x - 5) hours.

For the second leg of the journey (with the current), the distance is 180 km and the speed is (x + 5) km/h. So, the time taken is 180 / (x + 5) hours.

The total time taken for the entire journey is given as 18 hours. So, we can write the equation:

(240 / (x - 5)) + (180 / (x + 5)) = 18

To solve this equation, we can multiply both sides by (x - 5)(x + 5) to eliminate the denominators:

240(x + 5) + 180(x - 5) = 18(x - 5)(x + 5)

Simplifying the equation:

240x + 1200 + 180x - 900 = 18(x^2 - 25)

420x + 300 = 18x^2 - 450

18x^2 - 420x - 750 = 0

Dividing both sides by 6 to simplify the equation:

3x^2 - 70x - 125 = 0

Now we can solve this quadratic equation to find the value of x.

Using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a)

where a = 3, b = -70, and c = -125.

Plugging in the values:

**x =