Question

Расстояние от пристани A до пристани B катер проплыл за 6 ч, а от пристани B до пристани A-за 7,5 ч.Скорость течения реки 2 км/ч.Найдите собственную скорость катера

Answer 1

Пусть V катера-x км\ч, тогда V по течению-x+2км\ч.Известно туда плыл за 6 часов, а обратно-7,5 часов. Составим уравнение
6*(x+2)=7.5 (x-2)
6x+ 12=7.5x+15
6x-7.5=15+12
1.5x=27
x=18

Answer 2

Calculation of the Boat's Speed

To find the boat's speed, we need to consider the time it took for the boat to travel from port A to port B and from port B to port A, as well as the speed of the river's current.

Given: - The boat took 6 hours to travel from port A to port B. - The boat took 7.5 hours to travel from port B to port A. - The speed of the river's current is 2 km/h.

Let's assume the boat's speed is represented by x km/h.

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

Distance = Speed × Time

Boat's Speed from Port A to Port B

When the boat is traveling from port A to port B, it is moving against the current. Therefore, the effective speed of the boat will be the difference between its speed and the speed of the current.

The distance from port A to port B can be calculated using the time and the effective speed:

Distance AB = (x - 2) km/h × 6 h

Boat's Speed from Port B to Port A

When the boat is traveling from port B to port A, it is moving with the current. Therefore, the effective speed of the boat will be the sum of its speed and the speed of the current.

The distance from port B to port A can be calculated using the time and the effective speed:

Distance BA = (x + 2) km/h × 7.5 h

Equating the Distances

Since the distance from port A to port B is the same as the distance from port B to port A, we can equate the two distances:

(x - 2) × 6 = (x + 2) × 7.5

Simplifying the equation:

6x - 12 = 7.5x + 15

6x - 7.5x = 12 + 15

-1.5x = 27

x = -27 / -1.5

x = 18

Therefore, the boat's speed is 18 km/h.

Please note that the negative sign in the equation is due to the direction of the current. The boat's speed is positive, indicating its direction of travel.