Question

Помогите решить задачу Турист за 4 дня прошел менее 50 км.В 1 день он прошел одну седьмую всего расстояния,во 2 день одну третью,в третий день он прошел одну вторую.А в четвертый оставшееся расстояние.Сколько всего километров прошел турист,если известно,что длина пути выражается целым числом километра

Answer 1

1) 1/7 + 1/3 + 1/2 = 6/42 + 14/42 + 21/42 = 41/42 ( пути ) всего за три дня
2) 1 - ( 41/42 ) = 1/42 ( пути ) в четвёртый день
3) весь путь = 42 ( км )
В четвёртый день прошёл 1 км

Answer 2

Problem Analysis

The problem states that a tourist walked less than 50 km in 4 days. On the first day, the tourist walked one-seventh of the total distance. On the second day, the tourist walked one-third of the remaining distance. On the third day, the tourist walked one-half of the remaining distance. And on the fourth day, the tourist walked the remaining distance. We need to find the total distance the tourist walked.

Solution

Let's assume the total distance the tourist walked is x km.

According to the problem, the tourist walked one-seventh of the total distance on the first day, which is x/7 km.

On the second day, the tourist walked one-third of the remaining distance. The remaining distance after the first day is x - (x/7) km. Therefore, on the second day, the tourist walked (x - (x/7))/3 km.

On the third day, the tourist walked one-half of the remaining distance. The remaining distance after the second day is (x - (x/7)) - ((x - (x/7))/3) km. Therefore, on the third day, the tourist walked ((x - (x/7)) - ((x - (x/7))/3))/2 km.

Finally, on the fourth day, the tourist walked the remaining distance, which is (x - (x/7)) - ((x - (x/7))/3) - (((x - (x/7)) - ((x - (x/7))/3))/2) km.

We can now set up an equation to solve for x:

x/7 + (x - (x/7))/3 + ((x - (x/7)) - ((x - (x/7))/3))/2 + (x - (x/7)) - ((x - (x/7))/3) - (((x - (x/7)) - ((x - (x/7))/3))/2) = x

Simplifying the equation:

x/7 + 3(x - (x/7))/7 + 2((x - (x/7)) - ((x - (x/7))/3))/7 + 7(x - (x/7)) - 7((x - (x/7))/3) - 7(((x - (x/7)) - ((x - (x/7))/3))/2) = 7x/7

Simplifying further:

x/7 + 3x/7 - 3(x/7) + 2x/7 - 2(x/7) + 7x - 7(x/7) + 7(x/7)/3 - 7(x/7)/2 = 7x/7

Combining like terms:

x/7 + 3x/7 - 3x/7 + 2x/7 - 2x/7 + 7x - 7x/7 + 7x/21 - 7x/14 = 7x/7

Simplifying further:

x/7 + 3x/7 - 3x/7 + 2x/7 - 2x/7 + 7x - x + x/3 - x/2 = x

Combining like terms:

x/7 + 3x/7 - 3x/7 + 2x/7 - 2x/7 + 7x - x + x/3 - x/2 = x

x(1/7 + 3/7 - 3/7 + 2/7 - 2/7 + 7 - 1 + 1/3 - 1/2) = x

x(1/7 + 7/7 + 1/3 - 1/2) = x

x(1/7 + 7/7 + 2/6 - 3/6) = x

x(1/7 + 7/7 - 1/6) = x

x(6/42 + 42/42 - 7/42) = x

x(41/42) = x

Dividing both sides by x:

41/42 = 1

Therefore, the equation is true for any value of x. This means that the total distance the tourist walked can be any value.

Since the problem states that the total distance is expressed as a whole number of kilometers, we can conclude that there is not enough information given to determine the exact total distance the tourist walked.

In summary, the total distance the tourist walked cannot be determined with the information provided.

Answer: The total distance the tourist walked cannot be determined with the information provided.