Question

Теплоход проходит по течению реки до пункта назначения 165 км и после стоянки возвращается в пункт отправления. Найдите скорость течения, если скорость течения равно 26 км/ч, стоянка длится 5 часов, а в пункт отправления теплоход возвращается через 18 часов после отплытия из него. Помогите.

Answer 1

Объяснение:

Припустим, что скорость теплохода в неподвижной воде х.

Время движения теплохода в пункт назначения и обратно 18 - 5 = 13 ч.

Скорость теплохода за течением: (х + 4).

Скорость теплохода против течения: (х - 4).

165/(х+4) + 165/(х - 4) = 13;

165 *(х - 4) + 165 *(х + 4) = 13 *(х - 4) *(х + 4);

165 *х - 165 *4 + 165 *х + 165 *4 = 13 *(х^2 - 16);

330 *х = 13 *х^2 - 208;

13 *х^2 - 330 *х -208 = 0;

Решим квадратное уравнение.

D = 330^2 - 4 *13 *(-208) = 119716 = 346^2;

Найдем корни уравнения.

х = (330 ± 346)/2 *13;

Скорость не может быть отрицательной, поэтому корень уравнения будет только 1.

х = (330 + 346)/2 *13 = 26.

Ответ: скорость теплохода в не подвижной воде 26 км/ч.

Answer 2

Problem Analysis

We are given the following information: - The distance from the starting point to the destination is 165 km. - The speed of the current is 26 km/h. - The boat stays at the destination for 5 hours. - The boat returns to the starting point 18 hours after departing from it.

We need to find the speed of the current.

Solution

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

Speed = Distance / Time

Let's break down the journey into different parts:

1. From the starting point to the destination: - Distance: 165 km - Time: Unknown (let's call it T1) - Speed of the boat relative to the water: Unknown (let's call it V1)

2. From the destination back to the starting point: - Distance: 165 km - Time: Unknown (let's call it T2) - Speed of the boat relative to the water: Unknown (let's call it V2)

3. The boat stays at the destination for 5 hours.

4. The boat returns to the starting point 18 hours after departing from it.

Now, let's calculate the values for T1, T2, V1, and V2.

Calculation

1. From the starting point to the destination: - Distance: 165 km - Time: T1 - Speed of the boat relative to the water: V1

Using the formula Speed = Distance / Time, we can write the equation as: V1 = 165 / T1

2. From the destination back to the starting point: - Distance: 165 km - Time: T2 - Speed of the boat relative to the water: V2

Using the formula Speed = Distance / Time, we can write the equation as: V2 = 165 / T2

3. The boat stays at the destination for 5 hours.

4. The boat returns to the starting point 18 hours after departing from it.

Since the boat is moving against the current on the return journey, we can calculate the effective speed of the boat relative to the water by subtracting the speed of the current from the speed of the boat.

Let's assume the speed of the boat relative to the water on the return journey is V2' (V2 prime).

The effective speed of the boat relative to the water on the return journey is given by: V2' = V2 - 26 (since the speed of the current is 26 km/h)

We know that the boat returns to the starting point 18 hours after departing from it. So, the total time for the return journey is T2 + 18.

Using the formula Speed = Distance / Time, we can write the equation as: V2' = 165 / (T2 + 18)

Now, we can equate the two expressions for V2': V2 - 26 = 165 / (T2 + 18)

Simplifying the equation, we get: V2 = 165 / (T2 + 18) + 26 (Equation 1)

We also know that the boat stays at the destination for 5 hours. So, the total time for the journey from the starting point to the destination is T1 + 5.

Using the formula Speed = Distance / Time, we can write the equation as: V1 = 165 / (T1 + 5)

Since the boat is moving with the current on the journey from the starting point to the destination, the effective speed of the boat relative to the water is given by: V1' = V1 + 26 (since the speed of the current is 26 km/h)

We know that the boat returns to the starting point 18 hours after departing from it. So, the total time for the return journey is T2 + 18.

Using the formula Speed = Distance / Time, we can write the equation as: V1' = 165 / (T2 + 18)

Now, we can equate the two expressions for V1': V1 + 26 = 165 / (T2 + 18)

Simplifying the equation, we get: V1 = 165 / (T2 + 18) - 26 (Equation 2)

We have two equations (Equation 1 and Equation 2) with two unknowns (V1 and T2). We can solve these equations to find the values of V1 and T2.

Solving the Equations

Let's solve the equations using substitution.

From Equation 1: V2 = 165 / (T2 + 18) + 26

Substituting this value of V2 in Equation 2: 165 / (T2 + 18) - 26 = 165 / (T2 + 18) + 26

Simplifying the equation, we get: 165 / (T2 + 18) - 165 / (T2 + 18) = 26 + 26

Simplifying further, we get: 0 = 52

This equation is not possible. It means there is no solution that satisfies both equations.

Conclusion

Based on the given information, it is not possible to determine the speed of the current. The equations derived from the given information lead to an inconsistent result.

Please let me know if there is anything else I can help you with.