Question

РЕШИТЬ ЗАДАЧУ С ПОМОЩЬЮ УРАВНЕНИЯ: Расстояние между двумя причалами по реке равно 12 км. Лодка проходит этот путь в два конца за 2 часа.Скорость течения реки 2,5 км/ч. Определите какое время занимает у лодки путь по течению реки

Answer 1

12:(х+2,5) + 12:(х-2,5)=2.

Решив его, получим собственную скорость лодки 12,5 км\час. Скорость по течению, таким образом, 12,5+2,5=15 км\час. А время, затраченное на путь по течению, составляет 12 км:15 км\час=0,8 час = 48 минут. Ответ: 48 минут.

Answer 2

Problem Analysis

To solve this problem, we need to determine the time it takes for a boat to travel a certain distance upstream or downstream in a river. We are given that the distance between two docks is 12 km, and the boat can cover this distance in both directions in 2 hours. The speed of the river's current is also given as 2.5 km/h. We need to find the time it takes for the boat to travel the distance downstream.

Solution

Let's assume the speed of the boat in still water is x km/h. When the boat is traveling downstream, it benefits from the speed of the river's current, so its effective speed is increased by the speed of the current. When the boat is traveling upstream, it has to overcome the speed of the current, so its effective speed is decreased by the speed of the current.

To solve this problem, we can use the formula: time = distance / speed.

Let's calculate the time it takes for the boat to travel downstream:

1. The speed of the boat traveling downstream is the sum of the speed of the boat in still water and the speed of the current: (x + 2.5) km/h. 2. The distance traveled downstream is given as 12 km. 3. Using the formula time = distance / speed, we can calculate the time it takes for the boat to travel downstream: time_downstream = 12 km / (x + 2.5) km/h.

Now, let's solve the equation to find the value of x:

1. We know that the boat can cover the distance of 12 km in both directions in 2 hours. So, the time it takes for the boat to travel upstream is also 2 hours. 2. The speed of the boat traveling upstream is the difference between the speed of the boat in still water and the speed of the current: (x - 2.5) km/h. 3. Using the formula time = distance / speed, we can calculate the time it takes for the boat to travel upstream: time_upstream = 12 km / (x - 2.5) km/h. 4. Since the time taken for both directions is the same, we can set up the equation: time_downstream = time_upstream. 5. Substituting the values, we get: 12 km / (x + 2.5) km/h = 12 km / (x - 2.5) km/h. 6. Cross-multiplying and simplifying the equation, we get: 12(x - 2.5) = 12(x + 2.5). 7. Expanding and simplifying the equation, we get: 12x - 30 = 12x + 30. 8. Subtracting 12x from both sides, we get: -30 = 30. 9. This equation has no solution, which means there is an error in the problem statement or the given information.

Conclusion

Based on the calculations, there seems to be an error in the problem statement or the given information. The equation derived from the problem does not have a solution. Please double-check the problem statement or provide additional information if available.