Question

Моторная лодка прошла 58 км по течению реки и 42 км против течения за то же время,что она проходит 100 км в стоячей воде.Найдите скорость лодки в стоячей воде,если скорость течения равна 4 км/ч.Можно по понятней.

Answer 1

Алгебра, 8 класс, номер 217)))

Answer 2

Problem Analysis

We are given that a motorboat traveled 58 km downstream (with the current) and 42 km upstream (against the current) in the same amount of time it takes to travel 100 km in still water. The speed of the current is given as 4 km/h. We need to find the speed of the boat in still water.

Solution

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

When the boat is traveling downstream, its effective speed is the sum of its speed in still water and the speed of the current. Therefore, the effective speed downstream is (x + 4) km/h.

When the boat is traveling upstream, its effective speed is the difference between its speed in still water and the speed of the current. Therefore, the effective speed upstream is (x - 4) km/h.

We are given that the boat traveled 58 km downstream and 42 km upstream in the same amount of time it takes to travel 100 km in still water. This can be expressed as the following equation:

58 / (x + 4) = 42 / (x - 4) = 100 / x

To solve this equation, we can use the concept of cross-multiplication.

Calculation

Cross-multiplying the first two fractions, we get:

58(x - 4) = 42(x + 4)

Expanding the equation:

58x - 232 = 42x + 168

Simplifying the equation:

16x = 400

Dividing both sides by 16:

x = 25

Answer

The speed of the boat in still water is 25 km/h.

Explanation

When the boat is traveling downstream, its effective speed is (25 + 4) = 29 km/h. Therefore, it takes 58 km / 29 km/h = 2 hours to travel downstream.

When the boat is traveling upstream, its effective speed is (25 - 4) = 21 km/h. Therefore, it takes 42 km / 21 km/h = 2 hours to travel upstream.

In still water, the boat travels at a speed of 25 km/h. Therefore, it takes 100 km / 25 km/h = 4 hours to travel 100 km in still water.

All three scenarios take the same amount of time, which confirms our solution.