Question

Теплохід пройшов 3 год за течією річки та 2,6 год проти течії. Шлях, який пройшов теплохід за течією, на 20,4 км більший за шлях, пройдений ним проти течії. Знайдіть швидкість теплохода в стоячій воді, якщо швидкість течії дорівнює 1,5 км/год. А 30 км/год В 28 км/год С 25 км/год D 32 км/год

Answer 1

Відповідь:

Нехай швидкість теплохода в стоячій воді -  x км/год. Тоді швидкість теплохода за течією - x + 1,5 км/год, а швидкість теплохода проти течії - x - 1,5 км/год.

Розв'яжемо рівняння:
$3(x+1,5) = 2,6(x - 1,5)+20,4\\3x + 4,5 = 2,6x - 3,9 + 20,4\\3x - 2,6x = 16,5 - 4,5\\0,4x = 12\\x = \frac{12}{0,4}\\x = 30$
Відповідь: А) 30 км/год.

Answer 2

Problem Analysis

We are given that a boat traveled for 3 hours with the current of a river and 2.6 hours against the current. The distance traveled with the current is 20.4 km more than the distance traveled against the current. We need to find the speed of the boat in still water, given that the speed of the current is 1.5 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 the speed of the boat in still water and the speed of the current. Therefore, the distance traveled with the current can be calculated as:

distance with current = (speed with current) × (time with current)

Substituting the values given in the problem, we have:

distance with current = (x + 1.5) × 3

Similarly, 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 distance traveled against the current can be calculated as:

distance against current = (speed against current) × (time against current)

Substituting the values given in the problem, we have:

distance against current = (x - 1.5) × 2.6

We are also given that the distance traveled with the current is 20.4 km more than the distance traveled against the current. Therefore, we can write the following equation:

distance with current = distance against current + 20.4

Substituting the previously calculated expressions for the distances, we have:

(x + 1.5) × 3 = (x - 1.5) × 2.6 + 20.4

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

Solving the Equation

Expanding the equation, we get:

3x + 4.5 = 2.6x - 3.9 + 20.4

Simplifying the equation, we have:

0.4x = 19.8

Dividing both sides of the equation by 0.4, we get:

x = 49.5

Therefore, the speed of the boat in still water is 49.5 km/h.

Answer

The speed of the boat in still water is 49.5 km/h.