Question

Турист идет из одного города в другой, каждый день проходя больше, чем впредыдущий день, на одно и то же расстояние. Известно, что за первый день туристпрошел 9 километров. Определите, сколько километров прошел турист за четверты йдень, если весь путь он прошел за 10 дней, а расстояние между городами составляет 180 км.

Answer 1

1 день - 9 км.
2 день - 9+х км.
3 день - 9+2х км.
4 день - 9+3х км.
5 день - 9+4х км.
6 день - 9+5х км.
7 день - 9+6х км.
 
9+9+х+9+2х+9+3х+9+4х+9+5х+9+6х=180 км.
21х+54=180
21х=180-54
21х=126
х=126:21
х=6
9+3х=9+3*6=12*6=72 км.
Ответ: турист прошёл 72 км. за четвёртый день.

Answer 2

1 день - 9 км.
2 день - 9+х км.= 11
3 день - 9+2х км.=13
4 день - 9+3х км.=15
5 день - 9+4х км.=17
6 день - 9+5х км.=19
7 день - 9+6х км.=21
 8 день -9+7х =23
9 день -9+8х =25
10 день -9+9х=27 итого  за 10 дней180км
(9*10) + 45х= 180
90 +45х=180
45х=180-90
45х=90
х=2(км)
4 день 9+ 3х=9+6= 15км

Answer 3

To solve this problem, we can use a simple mathematical approach. Let's break down the information given:

- The tourist walks from one city to another every day, covering more distance each day than the previous day. - On the first day, the tourist walked 9 kilometers. - The entire journey took 10 days. - The distance between the cities is 180 kilometers.

To find out how many kilometers the tourist walked on the fourth day, we need to determine the daily increase in distance.

Calculating the Daily Increase:

Since the tourist covers more distance each day, we can assume that there is a constant daily increase in distance. Let's denote this daily increase as x.

On the first day, the tourist walked 9 kilometers. On the second day, the tourist walked 9 + x kilometers. On the third day, the tourist walked 9 + x + x kilometers. On the fourth day, the tourist walked 9 + x + x + x kilometers.

Simplifying the Equation:

We know that the entire journey took 10 days, so the sum of the distances covered on each day should be equal to the total distance between the cities, which is 180 kilometers.

Using this information, we can set up the equation:

9 + (9 + x) + (9 + x + x) + (9 + x + x + x) + ... = 180

Solving the Equation:

To solve this equation, we can use the formula for the sum of an arithmetic series:

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

Where: - S is the sum of the series - n is the number of terms in the series - a is the first term of the series - d is the common difference between terms

In our case, the first term (a) is 9, the common difference (d) is x, and the number of terms (n) is 10.

Plugging in these values, we get:

(10/2)(2*9 + (10-1)x) = 180

Simplifying further:

5(18 + 9x) = 180 90 + 45x = 180 45x = 90 x = 2

Finding the Distance on the Fourth Day:

Now that we have found the value of x, which is 2, we can calculate the distance the tourist walked on the fourth day.

On the fourth day, the distance covered is: 9 + x + x + x = 9 + 2 + 2 + 2 = 15 kilometers.

Therefore, the tourist walked 15 kilometers on the fourth day.

Please let me know if you need any further assistance!