Question

Моторная лодка прошла 7 км по течению реки и 10 км против течения,затратив на путь по течению на 0.5 ч меньше,чем на путь против течения .Собственная скорость лодки 12 км.ч.НАЙДИТЕ скорость лодки против течения!

Answer 1

х-это скорость течение реки.Тогда составим уравнение:

10:(х-12)-7:(х+12)=0,5 даем множитель каждому  решим уравнение.

Получим 3х+204/(х-12)(х+12)=0,5

тогда квадратное уранение получается 0,5 х(в квадрате)-3х-2276=0

Выйдет 2 корня: один будет положительным, а другой отрицательным. То положительное число будет вашим ответом.

 

 

Answer 2

Problem Analysis

We are given that a motorboat traveled 7 km downstream (with the current) and 10 km upstream (against the current). The time taken for the downstream journey was 0.5 hours less than the time taken for the upstream journey. The speed of the motorboat is given as 12 km/h. We need to find the speed of the motorboat against the current.

Solution

Let's assume the speed of the current is c km/h and the speed of the motorboat against the current is x km/h.

To find the speed of the motorboat against the current, we can use the formula:

Speed = Distance / Time

For the downstream journey: - Speed of the motorboat + Speed of the current = Speed of the boat downstream - (12 + c) km/h = 7 km / Time taken for the downstream journey

For the upstream journey: - Speed of the motorboat - Speed of the current = Speed of the boat upstream - (12 - c) km/h = 10 km / Time taken for the upstream journey

We are given that the time taken for the downstream journey is 0.5 hours less than the time taken for the upstream journey. So we can write:

Time taken for the downstream journey = Time taken for the upstream journey - 0.5 hours

Substituting the values into the equations, we get:

(12 + c) km/h = 7 km / (Time taken for the upstream journey - 0.5 hours) (12 - c) km/h = 10 km / Time taken for the upstream journey We can solve these two equations to find the value of c.

Let's solve the equations step by step:

From equation (12 + c) km/h = 7 km / (Time taken for the upstream journey - 0.5 hours)

Cross-multiplying, we get: (12 + c) km/h * (Time taken for the upstream journey - 0.5 hours) = 7 km

Expanding the equation, we get: 12 * (Time taken for the upstream journey - 0.5 hours) + c * (Time taken for the upstream journey - 0.5 hours) = 7

Simplifying the equation, we get: 12 * Time taken for the upstream journey - 6 + c * Time taken for the upstream journey - 0.5c = 7

Combining like terms, we get: (12 + c) * Time taken for the upstream journey - 6 - 0.5c = 7

From equation (12 - c) km/h = 10 km / Time taken for the upstream journey

Cross-multiplying, we get: (12 - c) km/h * Time taken for the upstream journey = 10 km

Expanding the equation, we get: 12 * Time taken for the upstream journey - c * Time taken for the upstream journey = 10

Simplifying the equation, we get: (12 - c) * Time taken for the upstream journey = 10

Now we have two equations: (12 + c) * Time taken for the upstream journey - 6 - 0.5c = 7 (12 - c) * Time taken for the upstream journey = 10 Let's solve these equations to find the value of c.

From equation (12 - c) * Time taken for the upstream journey = 10

Expanding the equation, we get: 12 * Time taken for the upstream journey - c * Time taken for the upstream journey = 10

Rearranging the equation, we get: 12 * Time taken for the upstream journey = c * Time taken for the upstream journey + 10

Dividing both sides of the equation by Time taken for the upstream journey, we get: 12 = c + 10 / Time taken for the upstream journey

Simplifying the equation, we get: c = 12 - 10 / Time taken for the upstream journey Now we can substitute the value of c from equation into equation to solve for Time taken for the upstream journey.

(12 + (12 - 10 / Time taken for the upstream journey)) * Time taken for the upstream journey - 6 - 0.5(12 - 10 / Time taken for the upstream journey)) = 7

Simplifying the equation, we get: (12 + (12 - 10 / Time taken for the upstream journey)) * Time taken for the upstream journey - 6 - 0.5(12 - 10 / Time taken for the upstream journey)) = 7

Expanding the equation, we get: 24 * Time taken for the upstream journey + (12 - 10 / Time taken for the upstream journey) * Time taken for the upstream journey - 6 - 0.5(12 - 10 / Time taken for the upstream journey)) = 7

Simplifying the equation, we get: 24 * Time taken for the upstream journey + 12 * Time taken for the upstream journey - 10 - 6 - 0.5(12 - 10 / Time taken for the upstream journey)) = 7

Combining like terms, we get: 36 * Time taken for the upstream journey - 16 - 0.5(12 - 10 / Time taken for the upstream journey)) = 7

Expanding the equation, we get: 36 * Time taken for the upstream journey - 16 - 6 + 5 / Time taken for the upstream journey = 7

Simplifying the equation, we get: 36 * Time taken for the upstream journey - 22 + 5 / Time