Question

По течению реки катер проходит расстояние между пристанями А и В за 7 часов а против течения за 9 часов скорость течения реки 5 километров в час какова собственная скорость катера?

Answer 1

Пусть Х-собст.скорость катера,
тогда по течению он пройдет расстояние от А до В (обзовем его У)
У=(Х+5) х 7
а против течения   У=(Х-5) х 9
Получаем уравнение:
7(Х+5)=9(Х-5)
7Х+35=9Х-45
2Х=45+35=80
Х=80:2
Х=40 км/ч

Answer 2

Calculation of the Boat's Speed

To calculate the boat's speed, we need to consider the time it takes for the boat to travel between the two piers in both directions.

Let's denote the boat's speed as x (in kilometers per hour).

When the boat is traveling downstream (with the current), it takes 7 hours to cover the distance between the piers A and B.

When the boat is traveling upstream (against the current), it takes 9 hours to cover the same distance.

We also know that the speed of the river's current is 5 kilometers per hour.

To calculate the boat's speed, we can use the formula:

Speed = Distance / Time

Let's denote the distance between the piers A and B as d (in kilometers).

When the boat is traveling downstream, the effective speed is the sum of the boat's speed and the speed of the current:

x + 5

Using the formula, we can write:

d = (x + 5) * 7 Similarly, when the boat is traveling upstream, the effective speed is the difference between the boat's speed and the speed of the current:

x - 5

Using the formula, we can write:

d = (x - 5) * 9 Now we have a system of two equations:

(x + 5) * 7 = d (x - 5) * 9 = d We can solve this system of equations to find the value of x, which represents the boat's speed.

Let's solve the system of equations:

(x + 5) * 7 = (x - 5) * 9

Expanding the equation:

7x + 35 = 9x - 45

Rearranging the equation:

2x = 80

Simplifying:

x = 40

Therefore, the boat's speed is 40 kilometers per hour.

Answer

The boat's own speed is 40 kilometers per hour.