Question

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

Answer 1

Пусть собственная скорость катера х км/ч.
Тогда его скорость:
из А в В будет (х+2)км/ч (по течению),
из В в А (х-2)км/ч. (против течения)
Путь, из А в В, 6*(х+2), а из В в А 7.5*(х-2).
Получаем уравнение
6*(х+2)=7.5*(х-2)
6х+12=7.5х-15
12+15=7.5х-6х
27=1.5х
х=18
Ответ: 18 км/ч собственная скорость катера. 

Answer 2

Calculation of the Boat's Speed

To find the boat's speed, we need to consider the distance traveled and the time taken for both legs of the journey. Let's denote the boat's speed as x km/h.

From the information given, we know that the boat traveled from port A to port B in 6 hours and from port B to port A in 7.5 hours. Additionally, we are told that the river's current has a speed of 2 km/h.

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

Distance = Speed × Time

Let's calculate the distance traveled from port A to port B and from port B to port A.

1. Distance from port A to port B: - The boat traveled from port A to port B in 6 hours. - The effective speed of the boat against the current is (x - 2) km/h, as the current is opposing the boat's motion. - Therefore, the distance from port A to port B can be calculated as (x - 2) × 6 km.

2. Distance from port B to port A: - The boat traveled from port B to port A in 7.5 hours. - The effective speed of the boat with the current is (x + 2) km/h, as the current aids the boat's motion. - Therefore, the distance from port B to port A can be calculated as (x + 2) × 7.5 km.

Now, we can set up an equation to find the value of x:

(x - 2) × 6 = (x + 2) × 7.5

Let's solve this equation to find the boat's speed.