Question

Расстояние между двумя пристанями равно 24 км. Двигаясь вниз по течению, катер проходит этот путь на 30 минут быстрее, чем в обратном направлении. Найдите собственную скорость катера, если скорость течения реки равна 2 км/ч.

Answer 1

х - собственная скорость катера

х + 2 - скорость катера по течению

х - 2 - скорость катера против течения

24/(х - 2) - 24/(х + 2) = 0,5 - уравнение

24·(х + 2) - 24(х - 2) = 0,5(х² - 4)

24х + 48 - 24х + 48 = 0,5х² - 2

0,5х²  = 98

х² = 196

х = 14

Ответ: собственная скорость катера 14км/ч

Answer 2

Problem Analysis

We are given that the distance between two piers is 24 km. A boat traveling downstream covers this distance in 30 minutes less time than it takes to travel the same distance upstream. The speed of the river current is given as 2 km/h. We need to find the speed of the boat.

Solution

Let's assume the speed of the boat is B km/h.

When the boat is traveling downstream, its effective speed is the sum of its own speed and the speed of the river current. So, the effective speed is (B + 2) km/h.

When the boat is traveling upstream, its effective speed is the difference between its own speed and the speed of the river current. So, the effective speed is (B - 2) km/h.

We are given that the boat takes 30 minutes less time to travel downstream compared to upstream. This means the time taken downstream is 30 minutes (or 0.5 hours) less than the time taken upstream.

Using the formula time = distance / speed, we can set up the following equation:

24 / (B + 2) = 24 / (B - 2) + 0.5

Let's solve this equation to find the value of B.

Calculation

To solve the equation, we can cross-multiply and simplify:

24(B - 2) = 24(B + 2) + 0.5(B + 2)(B - 2)

Simplifying further:

24B - 48 = 24B + 48 + 0.5(B^2 - 4)

Simplifying again:

24B - 48 = 24B + 48 + 0.5B^2 - 2

Combining like terms:

-48 = 48 + 0.5B^2 - 2

Simplifying:

-96 = 0.5B^2

Dividing both sides by 0.5:

-192 = B^2

Taking the square root of both sides:

B = ±√(-192)

Since we are dealing with speeds, the speed cannot be negative. Therefore, we can ignore the negative solution.

B = √(-192)

Answer

The speed of the