Question

За 5 год за течією річки теплохід проходить такий самий шлях, як за 6 год проти течії. Знайди власну швидкість теплохода, якщо швидкість течії річкидорівнює 2,5 км/год. Яке з рівнянь відповідає умові задачі, якщо через Xпозначено власну швидкість теплохода? *молюююю помогите срочно очень!!!!​

Answer 1

Ответ:

27,5 км/ час -скорость теплохода

Пошаговое объяснение:

Пусть скорость теплохода= х км/час, тогда:

5(х+2,5)= 6(х-2,5)

5х+12,5=6х-15

х=27,5 (км/час) скорость теплохода

Answer 2

Problem Analysis

We are given that a boat takes the same amount of time to travel a certain distance downstream in 5 hours as it does to travel the same distance upstream in 6 hours. We are also given that the speed of the river current is 2.5 km/h. We need to find the speed of the boat.

Solution

Let's assume the speed of the boat is X km/h.

When the boat is traveling downstream, its effective speed is the sum of its own speed and the speed of the river current. Therefore, the effective speed is (X + 2.5) km/h.

When the boat is traveling upstream, its effective speed is the difference between its own speed and the speed of the river current. Therefore, the effective speed is (X - 2.5) km/h.

We are given that the boat takes 5 hours to travel the distance downstream and 6 hours to travel the same distance upstream. We can use the formula distance = speed × time to set up two equations:

1. Distance downstream = (X + 2.5) km/h × 5 hours 2. Distance upstream = (X - 2.5) km/h × 6 hours

Since the distance traveled is the same in both cases, we can set these two equations equal to each other:

(X + 2.5) × 5 = (X - 2.5) × 6

Now, let's solve this equation to find the value of X, which represents the speed of the boat.

Solving the Equation

Expanding the equation, we get:

5X + 12.5 = 6X - 15

Rearranging the terms, we get:

X - 6X = -15 - 12.5

Simplifying, we have:

-X = -27.5

Dividing both sides by -1, we get:

X = 27.5

Therefore, the speed of the boat is 27.5 km/h.

Conclusion

The speed of the boat is 27.5 km/h.