Question

Моторная лодка прошла против течения реки 60 км и вернулась в пункт отправления, затратив на обратный путь на 45 минут меньше. Найдите скорость лодки в неподвижной воде, если скорость течения равна 2 км/ч. Ответ дайте в км/ч.

Answer 1

х км/ч - собственная скорость лодки

(х-2) км/ч - скорость лодки против течения

(х+2) - скорость по течению

t=S:V

60/(х-2) - 60/(х+2)=0,75

60х+120-60х+120=0,75х²-3

0,75х²=243

х=√243

х=18(км/ч) - скорость лодки в неподвижной воде.

Answer 2

Problem Analysis

We are given that a motorboat traveled against the current of a river for 60 km and then returned to the starting point, spending 45 minutes less on the return journey. We need to find the speed of the boat in still water, given that the speed of the current is 2 km/h.

Solution

Let's assume the speed of the boat in still water is x km/h. The speed of the current is given as 2 km/h.

When the boat is traveling against the current, its effective speed is reduced by the speed of the current. So, the boat's speed against the current is (x - 2) km/h.

When the boat is traveling with the current, its effective speed is increased by the speed of the current. So, the boat's speed with the current is (x + 2) km/h.

We are given that the boat traveled 60 km against the current and spent 45 minutes less on the return journey. Let's convert 45 minutes to hours: 45 minutes = 45/60 = 0.75 hours.

Now, we can set up the equation based on the given information:

Distance traveled against the current = Distance traveled with the current

Using the formula distance = speed × time, we can write:

(x - 2) × (60) = (x + 2) × (60 - 0.75)

Simplifying the equation:

60x - 120 = 60x + 117

Subtracting 60x from both sides:

-120 = 117

This equation is not possible to solve because it leads to a contradiction. It means there is no solution for the speed of the boat in still water that satisfies the given conditions.

Therefore, there is no valid answer to this problem.

Answer

There is no valid answer to this problem.