Question

Моторная лодка проходит расстояние против течения за 7 часов, а по течению это же расстояние за 3 часа. Найти скорость течения, если скорость лодки в стоячей воде 8км/ч

Answer 1

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Answer 2

Problem Analysis

We are given that a motorboat takes 7 hours to travel a certain distance against the current, and the same distance can be covered in 3 hours when traveling with the current. We need to find the speed of the current, given that the speed of the boat in still water is 8 km/h.

Solution

Let's assume the speed of the current is x km/h.

When the boat is traveling against the current, its effective speed is the difference between the speed of the boat in still water and the speed of the current. Therefore, the effective speed is 8 - x km/h.

Similarly, when the boat is traveling with the current, its effective speed is the sum of the speed of the boat in still water and the speed of the current. Therefore, the effective speed is 8 + x km/h.

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

When traveling against the current, the distance is (8 - x) × 7 km.

When traveling with the current, the distance is (8 + x) × 3 km.

Since the distances are the same, we can set up the following equation:

(8 - x) × 7 = (8 + x) × 3

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

Calculation

Expanding the equation, we have:

56 - 7x = 24 + 3x

Combining like terms, we get:

10x = 32

Dividing both sides by 10, we find:

x = 3.2

Answer

The speed of the current is 3.2 km/h.

Explanation

When the boat is traveling against the current, its effective speed is 8 - 3.2 = 4.8 km/h. This allows it to cover the distance in 7 hours.

When the boat is traveling with the current, its effective speed is 8 + 3.2 = 11.2 km/h. This allows it to cover the same distance in 3 hours.

Therefore, the speed of the current is 3.2 km/h.