Question

Расстояние между двумя пунктами катер прошел по течению реки за 7 часов, а против течения - за 8 часов.Найдите скорость лодки если скорость течения реки равна 3,5 км/ч

Answer 1

Х собственная скорость
х+3,5 скорость по течению
х-3,5 против течения
8(х-3,5)=7(х+3,5)
8х-28=7х+24,5
х=52,5км/час собственная скорость

Answer 2

Problem Analysis

We are given that a boat traveled a certain distance in 7 hours with the current of a river and in 8 hours against the current. We need to find the speed of the boat given that the speed of the river current is 3.5 km/h.

Solution

Let's assume the speed of the boat in still water is x km/h.

When the boat is traveling with the current, its effective speed is the sum of the boat's speed and the speed of the current. Therefore, the boat's effective speed is (x + 3.5) km/h.

When the boat is traveling against the current, its effective speed is the difference between the boat's speed and the speed of the current. Therefore, the boat's effective speed is (x - 3.5) km/h.

We can use the formula distance = speed × time to calculate the distance traveled by the boat in both cases.

Let's denote the distance traveled with the current as d1 and the distance traveled against the current as d2.

From the given information, we have the following equations:

d1 = (x + 3.5) × 7 (1)

d2 = (x - 3.5) × 8 (2)

To find the speed of the boat, we need to solve these equations simultaneously.

Solving the Equations

Let's solve equations (1) and (2) to find the value of x.

From equation (1), we can express x in terms of d1:

x = (d1 / 7) - 3.5 (3)

Substituting equation (3) into equation (2), we get:

(d1 / 7 - 3.5 - 3.5) × 8 = d2

Simplifying the equation:

(d1 / 7 - 7) × 8 = d2

Expanding and rearranging the equation:

8d1 / 7 - 56 = d2

Simplifying further:

8d1 - 56 × 7 = 7d2

8d1 - 392 = 7d2

Now, we have a relationship between d1 and d2. We can use this relationship to find the value of x.

Calculation

Let's calculate the value of x using the relationship between d1 and d2.

From the given information, we know that d1 = 7x and d2 = 8x.

Substituting these values into the relationship equation:

8(7x) - 392 = 7(8x)

Simplifying the equation:

56x - 392 = 56x

We can see that the variable x cancels out, which means that the equation is not solvable. This implies that there is no unique solution for the speed of the boat.

Conclusion

Based on the given information, we cannot determine the speed of the boat. The equations do not have a unique solution, which means that there are multiple possible values for the speed of the boat that satisfy the given conditions.

Please note that the calculations above assume a linear relationship between the speed of the boat and the distance traveled. In reality, the relationship may be more complex and depend on various factors such as the shape of the boat, the depth of the river, and other hydrodynamic factors.