Question

Турист идет из одного города в другой,каждый день проходя больше,чем в предыдущий день,на одно и то же расстояние.Известно,что за первый день турист прошел 8 км. Определите ,сколько км. прошел турист за пятый день,если весь путь он прошел за семь дней,а расстояние между городами составляет 119 км.

Answer 1

Допустим , что расстояние, которое турист прибавляет каждый день это х.
Тогда 1 день - 8 км; 2 день - 8+х км; 3 день - 8+2х км; 4 день - 8+3х км; 5 день - 8+4х км; 6 день - 8+5х км; 7 день - 8+6х км.
Отсюда: 8+8+х+8+2х+8+3х+8+4х+8+5х+8+6х=119
              21х+56=119
              21х=119-56
              21х=63
              х=63:21
              х=3
Находим сколько прошел турист за пятый день: 8+4х=8+4*3=8+12=20 (км турист прошел за пятый день)

Answer 2

Problem Analysis

The problem states that a tourist is walking from one city to another, and each day they walk more than the previous day by the same distance. It is known that on the first day, the tourist walked 8 km. The task is to determine how many kilometers the tourist walked on the fifth day, given that the entire journey took seven days and the distance between the cities is 119 km.

Solution

To solve this problem, we can use the concept of an arithmetic progression. In an arithmetic progression, each term is obtained by adding a constant difference to the previous term.

Let's denote the distance walked on the first day as a (8 km in this case) and the common difference between the distances walked on consecutive days as d. We need to find the distance walked on the fifth day.

We can use the formula for the nth term of an arithmetic progression to find the distance walked on the fifth day:

a₅ = a + (5 - 1) * d

Substituting the given values, we have:

a₅ = 8 + (5 - 1) * d

To find the common difference d, we can use the formula for the sum of an arithmetic progression:

S = (n/2) * (2a + (n - 1)d)

Substituting the given values, we have:

119 = (7/2) * (2 * 8 + (7 - 1)d)

Simplifying the equation, we get:

119 = 7 * (16 + 6d)

Solving for d, we have:

119 = 112 + 42d

42d = 119 - 112

42d = 7

d = 7/42

d = 1/6

Now, substituting the value of d back into the equation for the fifth term, we have:

a₅ = 8 + (5 - 1) * (1/6)

a₅ = 8 + 4/6

a₅ = 8 + 2/3

a₅ = 24/3 + 2/3

a₅ = 26/3

Therefore, the tourist walked 26/3 km on the fifth day.

Answer

The tourist walked 26/3 km on the fifth day.

Explanation

The distance walked on each day forms an arithmetic progression, where the first term is 8 km and the common difference is 1/6 km. Using the formula for the nth term of an arithmetic progression, we calculated that the distance walked on the fifth day is 26/3 km.