Question

Теплоход против течения реки за 5 часов проплыл такое же расстояние, что и за 3 часа по течению. Чему равна собственная скорость теплохода, если скорость течения реки 3,8км\ч?

Answer 1

Problem Analysis

We are given that a boat traveled the same distance against the current of a river in 5 hours as it did with the current in 3 hours. We need to determine the boat's own speed if the speed of the river's current is 3.8 km/h.

Solution

Let's assume the boat's own speed is x km/h.

When the boat is traveling against the current, its effective speed is the difference between its own speed and the speed of the current. So, the effective speed is (x - 3.8) km/h.

Similarly, when the boat is traveling with the current, its effective speed is the sum of its own speed and the speed of the current. So, the effective speed is (x + 3.8) km/h.

We are given that the boat traveled the same distance in both cases. Let's denote the distance as d km.

Using the formula speed = distance / time, we can set up the following equations:

1. When traveling against the current: (x - 3.8) = d / 5 2. When traveling with the current: (x + 3.8) = d / 3

We can solve these equations to find the value of x.

Solving the Equations

Let's solve the equations using algebraic manipulation.

From equation 1, we have x - 3.8 = d / 5. Rearranging the equation, we get d = 5(x - 3.8).

Substituting this value of d into equation 2, we have (x + 3.8) = (5(x - 3.8)) / 3.

Simplifying the equation, we get 3(x + 3.8) = 5(x - 3.8).

Expanding and rearranging the equation, we have 3x + 11.4 = 5x - 19.

Simplifying further, we get 2x = 30.4.

Dividing both sides of the equation by 2, we find x = 15.2.

Answer

Therefore, the boat's own speed is 15.2 km/h when the speed of the river's current is 3.8 km/h.

Conclusion

In this problem, we used the concept of relative speed to determine the boat's own speed when traveling against and with the current of a river. By setting up and solving equations, we found that the boat's own speed is 15.2 km/h.