Question

Города Волгоград и Астрахань расположены на берегу реки. Девочка поехала в гости к бабушке в Астрахань из Волгограда на теплоходе. Он прощел против течения реки 120 км и вернулась в Волгоград, затратив на обратный путь на 2 часа меньше. Найдите скорость теплохода в неподвижной воде, если скорость течения равна 1 км/ч. Ответ дайте в км/ч.

Answer 1

Х км/ч - собственная скорость теплохода
(х-1) км/ч - скорость против течения
(х+1) км/ч - скорость по течению
t=S:V
120/(х-1)-120/(х+1)=2
120х+120-120х+120=2х²-2
2х²=242
х²=121
х=11(км/ч) - собственная скорость теплохода.

Answer 2

Calculating the Speed of the Boat

To calculate the speed of the boat in still water, we can use the concept of relative speed. Let's denote the speed of the boat in still water as B and the speed of the river's current as C.

When the boat travels downstream (in the direction of the current), the effective speed is the sum of the boat's speed and the speed of the current: B + C. When the boat travels upstream (against the current), the effective speed is the difference between the boat's speed and the speed of the current: B - C.

Given that the boat traveled 120 km downstream and then 120 km upstream, and the time difference for the two trips was 2 hours, we can set up the following equation:

120 / (B + C) - 120 / (B - C) = 2

Let's solve for B.

Solving for the Speed of the Boat

Using the given information, we can solve for the speed of the boat in still water:

120 / (B + 1) - 120 / (B - 1) = 2

This equation can be solved to find the value of B.