Question

Лодка проходит по течению 12 км на 30 мин быстрее чем такое же расстояние против течения реки. найдите собственную скорость лодки если скорость течения реки 2 км/ч заранее спасибо

Answer 1

Пусть собственная скорость лодки - х.                 30 мин=0,5 ч.
12/(x-2)-12/(x+2)=0,5
12x+24-12x+24=0,5(x+2)(x-2)
0,5(x²-4)=48
x²-4=96
x²=100
x₁=10   x₂=-10∉
Ответ: собственная скорость лодки 10 км/ч.

Answer 2

Problem Analysis

We are given that a boat travels 12 km downstream in 30 minutes faster than 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 x 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 downstream is (x + 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 upstream is (x - 2) km/h.

We are given that the boat takes 30 minutes less time to travel 12 km downstream compared to traveling the same distance upstream.

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

12 / (x + 2) = 12 / (x - 2) + 30 minutes

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

12(x - 2) = 12(x + 2) + 30(x + 2)

Simplifying further:

12x - 24 = 12x + 24 + 30x + 60

Combining like terms:

12x - 12x - 30x = 24 + 60 + 24

Simplifying further:

-18x = 108

Dividing both sides by -18:

x = -6

Since the speed of the boat cannot be negative, we can conclude that there is no solution to this problem.

Therefore, there is no valid speed for the boat that satisfies the given conditions.

Please let me know if I can help you with anything else.