Question

Решить задачу с системой! Яхта проходит за 4 часа по течению реки такое же расстояние, какое за 5 часов против течения найдите собственную скорость лодки е сли скорость течения равна 3 км/ч.

Answer 1

Скорость по течению v+3 , против v-3
S=vt , v=S\t
по течению: v+3=S\4 , против v-3=S\5 
Система: {4v+12=S
               {5v-15=S
{4v-S=-12
{5v-S=15

{-4v+S=12
{5v-S=15

{v=27
{S=120
ответ:27 км\ч

Answer 2

Problem Analysis

To solve this problem, we need to find the speed of the boat in still water. We are given that the boat takes 4 hours to travel a certain distance with the current and 5 hours to travel the same distance against the current. The speed of the current is given as 3 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 its speed in still water and the speed of the current. So, the effective speed is (x + 3) km/h.

When the boat is traveling against the current, its effective speed is the difference between its speed in still water and the speed of the current. So, the effective speed is (x - 3) km/h.

We are given that the boat takes 4 hours to travel a certain distance with the current and 5 hours to travel the same distance against the current. Let's use the formula distance = speed × time to set up two equations:

1. Distance traveled with the current: (x + 3) × 4 2. Distance traveled against the current: (x - 3) × 5

Since the distances traveled in both cases are the same, we can set up the following equation:

(x + 3) × 4 = (x - 3) × 5

Now, let's solve this equation to find the value of x, which represents the speed of the boat in still water.

Calculation

Expanding the equation, we get:

4x + 12 = 5x - 15

Rearranging the equation, we get:

x = 27

Answer

The speed of the boat in still water is 27 km/h.

Verification

To verify our answer, let's substitute the value of x into the equation:

(27 + 3) × 4 = (27 - 3) × 5

30 × 4 = 24 × 5

120 = 120

The equation holds true, which confirms that our answer is correct.