Question

За 6 часов катер проходит по течению на 10 км меньше, чем за 10 ч. против течения. Какова скорость течения если собственная скорость катера 15 км/ч?

Answer 1

3,125 километров в час

Answer 2

Problem Analysis

We are given that a boat travels 10 km less in 6 hours with the current than it does in 10 hours against the current. We need to find the speed of the current given that the boat's own speed is 15 km/h.

Solution

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

When the boat is traveling with the current, its effective speed is reduced by the speed of the current. So, the boat's speed with the current is 15 - x km/h.

According to the problem, the boat travels 10 km less in 6 hours with the current compared to 10 hours against the current.

Using the formula distance = speed × time, we can set up the following equation:

(15 - x) × 6 = 15 × 10 - 10x

Let's solve this equation to find the value of x.

Calculation

Expanding the equation:

90 - 6x = 150 - 10x

Rearranging the terms:

10x - 6x = 150 - 90

4x = 60

Dividing both sides by 4:

x = 15

Answer

The speed of the current is 15 km/h.

Explanation

The boat's speed with the current is 15 - 15 = 0 km/h. This means that the boat is stationary when traveling with the current. Therefore, the boat does not make any progress and travels 10 km less in 6 hours compared to 10 hours against the current.

Please note that the speed of the current is equal to the speed of the boat in this case.