Question

10. Розв'яжи задачу разом з роботом «Агент Z». Від пристані Щастя відійшов катер. Він дійшов до при- стані Мрія та повернувся назад, затративши на весь шлях 9 год. Від пристані Щастя катер рухався зі швидкістю 25 км/год, а на зворотному шляху його швидкість становила 20 км/год. Визнач від- стань від однієї пристані до другої. БУДЬ ЛАСКА ШВИДШЕ, ДУЖЕ ПОТРІБНО, ДАЮ МАКСИМУМ БАЛІВ, ЯКЩО ПРАВИЛЬНО

Answer 1

Ответ:

расстояние между пристанями равно 100км

Пошаговое объяснение:

Используем формулу S=v*t

Пусть время на движение от Счастья до Мечты равно t часов.

Тогда от Счастья до Мечты путь    S₁ = 25t км

Время от Мечты до Счастья             (9-t) часов.

Тогда  от Мечты до Счастья путь  S₂ = 20(9-t) км

И эти пути равны   S₁ = S₂ по условию.

Составим и решим уравнение

25t = 20(9-t)

25t = 180-20t

45t = 180

t = 4

Вернемся к нашим обозначениям и получим, что  время на движение от Счастья до Мечты равно 4 часа.

Тогда расстояние между пристанями равно

(25км/час * 4 час) = 100км

Answer 2

To solve this problem, we need to find the distance between the two ports, given the speed of the boat on the forward and return journeys and the total time taken.

Let's denote the distance between the ports as "d" (in kilometers). We are given that the boat traveled at a speed of 25 km/h on the forward journey and 20 km/h on the return journey. The total time taken for the entire trip is 9 hours.

To find the distance, we can use the formula:

Distance = Speed × Time

On the forward journey, the boat traveled at a speed of 25 km/h. Let's denote the time taken for the forward journey as "t1" (in hours). Using the formula above, we can write:

25 × t1 = d

On the return journey, the boat traveled at a speed of 20 km/h. Let's denote the time taken for the return journey as "t2" (in hours). Using the formula again, we can write:

20 × t2 = d

We are also given that the total time taken for the entire trip is 9 hours. Therefore, we can write:

t1 + t2 = 9

Now we have a system of equations with three unknowns (d, t1, and t2). We can solve this system to find the values of these variables.

To solve the system, we can use the substitution method. Let's solve the first equation for t1:

t1 = d / 25

Substituting this value of t1 into the third equation, we get:

(d / 25) + t2 = 9

Simplifying this equation, we have:

d + 25t2 = 225

Now, let's solve the second equation for t2:

t2 = d / 20

Substituting this value of t2 into the third equation, we get:

t1 + (d / 20) = 9

Simplifying this equation, we have:

20t1 + d = 180

Now we have two equations with two unknowns (d and t1). We can solve this system to find the values of these variables.

Let's solve the first equation for d:

d = 225 - 25t2

Substituting this value of d into the second equation, we get:

20t1 + (225 - 25t2) = 180

Simplifying this equation, we have:

20t1 - 25t2 = -45

Now we have two equations with two unknowns (t1 and t2). We can solve this system to find the values of these variables.

Multiplying the second equation by 4, we get:

80t1 - 100t2 = -180

Adding this equation to the previous equation, we eliminate t1:

80t1 - 100t2 + 20t1 - 25t2 = -45 + (-180)

Simplifying this equation, we have:

100t1 - 125t2 = -225

Dividing this equation by 25, we get:

4t1 - 5t2 = -9

Now we have a new equation with two unknowns (t1 and t2). We can solve this equation to find the values of these variables.

Let's solve the first equation for t1:

t1 = (5t2 - 9) / 4

Substituting this value of t1 into the second equation, we get:

20((5t2 - 9) / 4) - 25t2 = -45

Simplifying this equation, we have:

25t2 - 45 - 25t2 = -45

Simplifying further, we have:

-45 = -45

This equation is true for any value of t2. Therefore, t2 can take any value.

Now, let's find the value of t1 using the equation we derived earlier:

t1 = (5t2 - 9) / 4

Since t2 can take any value, t1 can also take any value.

Therefore, there are infinitely many solutions to this problem. The distance between the two ports can vary depending on the values of t1 and t2.

Please note that this solution assumes constant speeds throughout the journey and does not take into account factors such as changes in current or wind speed, which may affect the actual distance traveled.