Question

1. Туристи пішли в похід. В перший день вони пройшли 1/3 всього шляху, за другий день 1/3 залишку, а в третій день 1/3 нового залишку. В результаті їм залишилось пройти 32 км. Скільки кілометрів складав весь маршрут?

Answer 1

1-1/3=2/3 шляху залишилось пройти після першого дня
2/3*1/3=2/9 пройшли другого дня
2/3-2/9=4/9 залишилось пройти після перших двох днів
4/9*1/3=4/27 пройшли третього дня
4/9-4/27=8/27 залишилось пройти після трьох днів
32:8/27=108 км весь шлях
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Answer 2

Calculation of the Total Distance of the Route

To calculate the total distance of the route, we need to determine the distances covered on each day and add them together.

Let's assume the total distance of the route is represented by x kilometers.

According to the given information: - On the first day, the group covered 1/3 of the total distance, which is x/3 kilometers. - On the second day, they covered 1/3 of the remaining distance, which is (2/3) * (x - x/3) = 2x/9 kilometers. - On the third day, they covered 1/3 of the remaining distance, which is (2/3) * (x - 2x/9) = 4x/27 kilometers.

The sum of these distances is equal to the remaining distance of 32 kilometers: x/3 + 2x/9 + 4x/27 = 32

To solve this equation, we can find a common denominator and combine the fractions: (9x + 6x + 4x)/27 = 32 19x/27 = 32

To isolate x, we can multiply both sides of the equation by 27/19: x = (32 * 27) / 19

Now, let's calculate the value of x: x = 432/19 ≈ 22.74

Therefore, the total distance of the route is approximately 22.74 kilometers.

Please note that the sources provided do not contain relevant information for this specific calculation. The solution is derived from mathematical calculations based on the given information.