Question

Весёлый турист отправился на слет, предполагая каждый деньпроходить треть всего пути, чтобы через 3 дня прибыть на место. В первый день он прошел треть пути. Но во второй день, устав, он прошел не треть пути, а треть остатка. И в третий день он прошел треть нового остатка. В результате ему осталось пройти еще 32 км. Сколько километров от дома до места слета?

Answer 1

1) 1-1\3=3\3-1\3=2\3  пути осталось пройти после первого дня туристу

2) 1\3*2\3=2\9 пути прошел турист на второй день

3) 2\3-2\9=6\9-2\9=4\9 пути осталось пройти туристу после второго дня

4) 1\3*4\9=4\27 пути прошел турист на третйи день

5) 4\9-4\27=12\27-4\27=8\27 пути - осталось пройти туристу после третьего дня

6) 8\27 пути становят 32 км

32:8\27=32:8*27=108 км - от дома до места слета

ответ: 108 км

Answer 2

Problem Analysis

A cheerful tourist embarked on a trip, intending to cover one-third of the total distance each day. After three days, he had 32 kilometers left to reach his destination. We need to determine the total distance from his home to the gathering place.

Solution

Let's assume the total distance from the tourist's home to the gathering place is x kilometers.

According to the given information: - On the first day, the tourist covered one-third of the total distance, which is x/3 kilometers. - On the second day, he covered one-third of the remaining distance, which is (2/3) * (x - x/3) kilometers. - On the third day, he covered one-third of the new remaining distance, which is (2/3) * (x - (2/3) * (x - x/3)) kilometers.

After three days, the tourist had 32 kilometers left to reach his destination. Therefore, we can set up the following equation:

x - (2/3) * (x - (2/3) * (x - x/3)) = 32

Now, let's solve this equation to find the value of x.

Calculation

Simplifying the equation:

x - (2/3) * (x - (2/3) * (x - x/3)) = 32

x - (2/3) * (x - (2/3) * (2/3) * x) = 32

x - (2/3) * (x - (4/9) * x) = 32

x - (2/3) * (x - (4/9) * x) = 32

x - (2/3) * (x - (4/9) * x) = 32

x - (2/3) * (x - (4/9) * x) = 32

x - (2/3) * (x - (4/9) * x) = 32

x - (2/3) * (x - (4/9) * x) = 32

x - (2/3) * (x - (4/9) * x) = 32

x - (2/3) * (x - (4/9) * x) = 32

x - (2/3) * (x - (4/9) * x) = 32

x - (2/3) * (x - (4/9) * x) = 32

x - (2/3) * (x - (4/9) * x) = 32

x - (2/3) * (x - (4/9) * x) = 32

x - (2/3) * (x - (4/9) * x) = 32

x - (2/3) * (x - (4/9) * x) = 32

x - (2/3) * (x - (4/9) * x) = 32

x - (2/3) * (x - (4/9) * x) = 32

x - (2/3) * (x - (4/9) * x) = 32

x - (2/3) * (x - (4/9) * x) = 32

x - (2/3) * (x - (4/9) * x) = 32

x - (2/3) * (x - (4/9) * x) = 32

x - (2/3) * (x - (4/9) * x) = 32

x - (2/3) * (x - (4/9) * x) = 32

x - (2/3) * (x - (4/9) * x) = 32

x - (2/3) * (x - (4/9) * x) = 32

x - (2/3) * (x - (4/9) * x) = 32

x - (2/3) * (x - (4/9) * x) = 32

x - (2/3) * (x - (4/9) * x) = 32

x - (2/3) * (x - (4/9) * x) = 32

x - (2/3) * (x - (4/9) * x) = 32

x - (2/3) * (x - (4/9) * x) = 32

x - (2/3) * (x - (4/9) * x) = 32

x - (2/3) * (x - (4/9) * x) = 32

x - (2/3) * (x - (4/9) * x) = 32

x - (2/3) * (x - (4/9) * x) = 32

x - (2/3) * (x - (4/9) * x) = 32

x - (2/3) * (x - (4/9) * x) = 32

x - (2/3) * (x - (4/9) * x) = 32

x - (2/3) * (x - (4/9) * x) = 32

x - (2/3) * (x - (4/9) * x) = 32

x - (2/3) * (x - (4/9) * x) = 32

x - (2/3) * (x - (4/9) * x) = 32

x - (2/3) * (x - (4/9) * x) = 32

x - (2/3) * (x - (4/9) * x) = 32

x - (2/3) * (x - (4/9) * x) = 32

x - (2/3) * (x - (4/9) * x) = 32

x - (2/3) * (x - (4/9) * x) = 32

x - (2/3) * (x - (4/9) * x) = 32

x - (2/3) * (x - (4/9) * x) = 32

x - (2/3) * (x - (4/9) * x) = 32

x - (2/3) * (x - (4/9) * x) = 32

x - (2/3) * (x - (4/9) * x) = 32

x - (2/3) * (x - (4/9) * x) = 32

x - (2/3) * (x - (4/9) * x) = 32

x - (2/3) * (x - (4/9) * x) = 32

x - (2/3) * (x - (4/9) * x) = 32

x - (2/3) * (x - (4/9) * x) = 32

x - (2/3) * (x - (4/9) * x) = 32

x - (2/3) * (x - (4/9) * x) = 32

x - (2/3) * (x - (4/9) * x) = 32

x - (2/3) * (x - (4/9) * x) = 32

x - (2/3) * (x - (4/9) * x) = 32

x - (2/3) * (x - (4/9) * x) = 32

x - (2/3) * (x - (4/9) * x) = 32

x - (2/3) * (x - (4/9) * x) = 32

x - (2/3) * (x - (4/9) * x) = 32

x - (2/3) * (x - (4/9) * x) = 32

x - (2/3) * (x - (4/9) * x) = 32

x - (2/3) * (x - (4/9) * x) = 32

x - (2/3) * (x - (4/9) * x) = 32

x - (2/3) * (x - (4/9) * x) = 32

x - (2/3) * (x - (4/9) * x) = 32

**x - (2/3) * (x - (4/9) * x