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

тур на лотосы в Астрахани из ВОлгограда

Answer 2

Calculation of the Speed of the Boat

To find the speed of the boat in still water, we need to use the information provided in the question. Let's break down the given information:

- The boat traveled 120 km against the current from Volgograd to Astrakhan. - The boat returned from Astrakhan to Volgograd, spending 2 hours less on the return journey. - The speed of the current is 1 km/h.

Let's assume the speed of the boat in still water is x km/h.

To calculate the speed of the boat, we can use the formula:

Speed of the boat in still water = (Distance traveled)/(Time taken)

Let's calculate the time taken for the boat to travel from Volgograd to Astrakhan and back:

- Distance from Volgograd to Astrakhan = 120 km - Time taken from Volgograd to Astrakhan = (Distance traveled)/(Speed of the boat - Speed of the current) - Time taken from Astrakhan to Volgograd = (Distance traveled)/(Speed of the boat + Speed of the current)

According to the question, the time taken for the return journey is 2 hours less than the time taken for the forward journey. Therefore, we can write the equation:

(Time taken from Astrakhan to Volgograd) = (Time taken from Volgograd to Astrakhan) - 2

Now, let's substitute the values into the equation:

(Distance traveled)/(Speed of the boat + Speed of the current) = (Distance traveled)/(Speed of the boat - Speed of the current) - 2

Simplifying the equation:

(Distance traveled)/(Speed of the boat + 1) = (Distance traveled)/(Speed of the boat - 1) - 2

Cross-multiplying:

(Distance traveled) * (Speed of the boat - 1) = (Distance traveled) * (Speed of the boat + 1) - 2 * (Distance traveled)

Simplifying further:

(Distance traveled) * (Speed of the boat - 1) = (Distance traveled) * (Speed of the boat + 1) - 2 * (Distance traveled)

(Distance traveled) * (Speed of the boat - 1) - (Distance traveled) * (Speed of the boat + 1) = -2 * (Distance traveled)

Speed of the boat - (Distance traveled) = -2

Speed of the boat = -2 + (Distance traveled)

Now, let's substitute the value of the distance traveled (120 km) into the equation:

Speed of the boat = -2 + 120

Speed of the boat = 118 km/h

Therefore, the speed of the boat in still water is 118 km/h.

Note: The negative value in the equation is due to the direction of the current. However, since speed cannot be negative, we take the positive value as the speed of the boat in still water.