Question

Биржа прошла по течкнию реки 72км и повернув обратно прошла еще 54 км затратила на ыесь путь 9часов найдите собственную скорость баржи если скорость течения реки равна 5км ч

Answer 1

Х ---- собственная скорость баржи;
Х + 5 --- скорость баржи ПО течению;
72/(Х+5) --- время пути по течению.
Х - 5 --- скорость баржи ПРОТИВ течения;
54/(Х-5) --- время пути против течения.
по условию, общее время 9 часов, т.е.:
9 = 72/(Х+5) + 54/(Х-5);
приводим к общему знаменателю (Х+5)(х-5) и умножаем на него все члены уравнения:
9*(Х+5)*(Х-5) = 72*(Х-5) + 54*(Х+5); 
9Х^2 - 225 = 72Х - 360 + 54Х + 270; 
9Х^2 - 126Х - 135 = 0; ( для удобства делим все члены уравнения на 9)
Х^2 - 14Х - 15 = 0  ( D= 14^2 +4*15 = 256; D>0, решаем дальше)
Х1 = [14 + V(256)] : 2 = (14+16) :2 = 15 (км/час)
(Х2 = [14 - V(256)] = (14-16):2 = -1 Отрицательный корень не берем,) 
Ответ: Собственная скорость баржи 15 км/час
Проверка: 72:(15+5) + 54:(15-5) =9;   9=9

Answer 2

Problem Analysis

We are given that a barge traveled downstream along a river for 72 km and then turned back and traveled upstream for another 54 km. The total time taken for the entire journey was 9 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 downstream, its effective speed is the sum of its own speed and the speed of the river current. So, the effective speed is (x + 5) km/h.

When the barge is traveling upstream, its effective speed is the difference between its own speed and the speed of the river current. So, the effective speed 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 downstream journey: - Distance = 72 km - Speed = (x + 5) km/h - Time = Distance / Speed = 72 / (x + 5) hours

For the upstream journey: - Distance = 54 km - Speed = (x - 5) km/h - Time = Distance / Speed = 54 / (x - 5) hours

The total time taken for the entire journey is given as 9 hours. So, we can write the equation:

(72 / (x + 5)) + (54 / (x - 5)) = 9

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

72(x - 5) + 54(x + 5) = 9(x + 5)(x - 5)

Simplifying the equation will give us the value of x, which represents the speed of the barge.

Let's solve the equation step by step:

72(x - 5) + 54(x + 5) = 9(x + 5)(x - 5) 72x - 360 + 54x + 270 = 9(x^2 - 25) 126x - 90 = 9x^2 - 225 9x^2 - 126x + 135 = 0

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

Quadratic Equation Solution

The quadratic equation is in the form ax^2 + bx + c = 0, where a = 9, b = -126, and c = 135.

Using the quadratic formula x = (-b ± √(b^2 - 4ac)) / (2a), we can find the values of x.

x = (-(-126) ± √((-126)^2 - 4 * 9 * 135)) / (2 * 9) x = (126 ± √(15876 - 4860)) / 18 x = (126 ± √(11016)) / 18 x = (126 ± 105.02) / 18

Simplifying further, we get two possible values for x:

x1 = (126 + 105.02) / 18 ≈ 13.28 km/h x2 = (126 - 105.02) / 18 ≈ 1.06 km/h

Since the speed of the barge cannot be negative, we can discard the second solution.

Therefore, the speed of the barge is approximately 13.28 km/h.

Answer

The speed of the barge is approximately 13.28 km/h.