Question

Лодка проплыла некоторое расстояние от пристани по течению реки и вернулась обратно, затратив на весь путь 8 ч. Собственная скорость лодки 8 км/ч, а скорость течения реки 2 км/ч. Определите,сколько времени плыла лодка по течению реки и все расстояние,которое она проплыла

Answer 1

Обозначим расстояние, пройденное лодкой в одну сторону = х.

Тогда имеем:

(х/10) + (х/6) = 8

 

(10 это скорость лодки при ее ходе по течению)

(6 - это скорость лодки при ее ходе против течения)

 

Решая уравнение, получаем: х=30.

 

Общее расстояние, пройденное лодкой = 30*2=60

Answer 2

Problem Analysis

We are given that a boat traveled a certain distance downstream and then returned to the starting point, taking a total of 8 hours for the entire journey. The boat's speed in still water is 8 km/h, and the speed of the river's current is 2 km/h. We need to determine how much time the boat spent traveling downstream and the total distance it covered.

Solution

Let's assume that the time taken by the boat to travel downstream is t hours. Since the boat is traveling with the current, its effective speed will be the sum of its speed in still water and the speed of the current, which is 8 km/h + 2 km/h = 10 km/h.

The time taken by the boat to travel upstream will be the same as the time taken to travel downstream, as the distance covered is the same. However, the boat's effective speed will be the difference between its speed in still water and the speed of the current, which is 8 km/h - 2 km/h = 6 km/h.

We can set up the following equation based on the given information:

Distance downstream / Speed downstream + Distance upstream / Speed upstream = Total time

Let's solve this equation to find the values of the distance downstream and the total distance covered.

Calculation

Let's denote the distance downstream as d km and the total distance covered as D km.

Using the equation mentioned above, we can write:

d / 10 + d / 6 = 8

Simplifying the equation:

6d + 10d = 480

16d = 480

d = 30

So, the distance downstream is 30 km.

The total distance covered will be twice the distance downstream:

D = 2 * d = 2 * 30 = 60 km

Therefore, the boat traveled downstream for t hours and covered a total distance of D km.

Answer

The boat traveled downstream for t hours, where t is the solution to the equation 30 / 10 + 30 / 6 = 8. The total distance covered by the boat is 60 km.