Question

Катер прошел по течению от пристани А до пристани В за 10 ч., а обратно от В до А за 12 ч.. За сколько часов плот доплывет от А до В?

Answer 1

Формула движения: S=v*t  

S - расстояние            x и y - скорость             t – время

y - скорость катера.

z - скорость течения (и плота).

y + z - скорость катера по течению.

x - z - скорость катера против течения.

S/(y + z) = 10 - время катера по течению.

S/z = х - время плота по течению (от А до В).

1) По условию задачи уравнение:

(y + z) * 10 = (y - z) * 12

10y +10z =12y- 12z

-2y = -22z

y= 11z

Найти расстояние S:

S=(y + z)*10 = 10y +10z = 11z*10+10z = 110z + 10z = 12z

 Найти время плота:

S/z = х - время плота 

x = 12z/z = 12ч

Ответ:12ч

Answer 2

Problem Analysis

We are given that a boat traveled downstream from port A to port B in 10 hours, and then traveled upstream from port B to port A in 12 hours. We need to determine how many hours it will take for the boat to travel from port A to port B.

Solution

Let's assume that the speed of the boat in still water is x units per hour, and the speed of the current is y units per hour.

When the boat is traveling downstream, the effective speed is the sum of the boat's speed and the current's speed. So, the boat's effective speed is (x + y) units per hour.

When the boat is traveling upstream, the effective speed is the difference between the boat's speed and the current's speed. So, the boat's effective speed is (x - y) units per hour.

We can set up the following equation based on the given information:

Downstream time = 10 hours Upstream time = 12 hours

Using the formula distance = speed × time, we can write the following equations:

Distance from A to B = (x + y) × 10 Distance from B to A = (x - y) × 12

Since the distance from A to B is the same as the distance from B to A, we can set up the following equation:

(x + y) × 10 = (x - y) × 12

Simplifying the equation:

10x + 10y = 12x - 12y 2x = 22y x = 11y

Now, we need to find the time it takes for the boat to travel from A to B. We can use the formula distance = speed × time again:

Distance from A to B = (x + y) × time

Substituting the value of x from the previous equation:

Distance from A to B = (11y + y) × time Distance from A to B = 12y × time

Since the distance from A to B is the same as the distance from B to A, we can set up the following equation:

12y × time = (x - y) × 12

Simplifying the equation:

12y × time = 12y time = 1 hour

Therefore, it will take the boat 1 hour to travel from port A to port B.

Answer

The boat will take 1 hour to travel from port A to port B.