Question

Пароход прошел по течению реки 48 км и столько же против течения, затратив на весь путь 5 ч. Найдите скорость парохода в стоячей воде, если скорость течения реки 4 км/ч. Решите, пожалуйста, с объяснением

Answer 1

Ответ:

Пошаговое объяснение:

Answer 2

Ответ:

20км/ч

Пошаговое объяснение:

S=48 км

t= 5 ч.

Vt= 4 км/ч.

V = скорость парохода

по течению время

S/(V+Vt)=48/(V+4)=t1

Против течения время

S/(V-Vt)=48/(V-4)=t2

Общее время

t=t1+t2

5=48/(V+4)+48/(V-4)

5=(48*(V+4) + 48*(V-4))/ ((V+4)*(V-4))

5*(V^2-16)=48*2V

5V^2-96V-80=0

V^2-11.2V+16=0

корни квадратного уравнения

V= -8 и V=20

Нам подходит только 20 км/ч  

проверка

48/(20+4) +48/(20-4)=5 часов.

Answer 3

Problem Analysis

We are given that a steamboat traveled 48 km upstream and the same distance downstream, taking a total of 5 hours for the entire journey. We are also given that the speed of the river's current is 4 km/h. We need to find the speed of the steamboat in still water.

Solution

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

When the steamboat is traveling upstream against the current, its effective speed is reduced by the speed of the current. Therefore, the speed of the steamboat relative to the ground is (x - 4) km/h.

When the steamboat is traveling downstream with the current, its effective speed is increased by the speed of the current. Therefore, the speed of the steamboat relative to the ground is (x + 4) km/h.

We are given that the steamboat traveled 48 km both upstream and downstream. We can use the formula distance = speed × time to calculate the time taken for each leg of the journey.

For the upstream journey: 48 km = (x - 4) km/h × t1 hours For the downstream journey: 48 km = (x + 4) km/h × t2 hours We are also given that the total time for the entire journey is 5 hours: t1 + t2 = 5 hours We can solve this system of equations to find the value of x, the speed of the steamboat in still water.

Solution Steps

1. Solve equation for t1: t1 = 48 km / (x - 4) km/h

2. Solve equation for t2: t2 = 48 km / (x + 4) km/h

3. Substitute the values of t1 and t2 into equation 48 km / (x - 4) km/h + 48 km / (x + 4) km/h = 5 hours

4. Multiply both sides of the equation by (x - 4)(x + 4) to eliminate the denominators: 48(x + 4) + 48(x - 4) = 5(x - 4)(x + 4)

5. Simplify the equation: 48x + 192 + 48x - 192 = 5(x^2 - 16)

6. Combine like terms: 96x = 5x^2 - 80

7. Rearrange the equation to form a quadratic equation: 5x^2 - 96x - 80 = 0

8. Solve the quadratic equation using factoring, completing the square, or the quadratic formula. The solutions are: x = 20 (ignoring the negative solution)

Therefore, the speed of the steamboat in still water is 20 km/h.

Answer

The speed of the steamboat in still water is 20 km/h.