Question

В первый день туристы прошли 3/17 всего пути во второй 8/51 всего пути в третий день 1/6 всего пути после чего осталось 255 км. Найти весь путь

Answer 1

3/17х+1/6х+8/51х+255=х
1/2х+255=х
255=1/2х
х=255*2=510 км

Answer 2

Problem Analysis

The problem states that on the first day, the tourists covered 3/17 of the total distance. On the second day, they covered 8/51 of the total distance. On the third day, they covered 1/6 of the total distance, after which 255 km remained. We need to find the total distance.

Solution

Let's assume the total distance is represented by the variable x.

According to the problem, the tourists covered 3/17 of the total distance on the first day. Therefore, the distance covered on the first day is (3/17) * x.

On the second day, they covered 8/51 of the total distance. Therefore, the distance covered on the second day is (8/51) * x.

On the third day, they covered 1/6 of the total distance. Therefore, the distance covered on the third day is (1/6) * x.

The sum of the distances covered on all three days should equal the total distance minus the remaining distance of 255 km.

So, we can set up the equation:

(3/17) * x + (8/51) * x + (1/6) * x + 255 = x

Now, we can solve this equation to find the value of x, which represents the total distance.

Calculation

Let's solve the equation:

(3/17) * x + (8/51) * x + (1/6) * x + 255 = x

To simplify the equation, we can find a common denominator for the fractions:

(3/17) * x + (8/51) * x + (1/6) * x + 255 = (17/17) * x

Multiplying both sides of the equation by 17 to eliminate the denominators:

3x + (8/3)x + (17/6)x + 255 * 17 = 17x

Simplifying the equation further:

18x + 8x + 17x + 4345 = 17x

Combining like terms:

43x + 4345 = 17x

Subtracting 17x from both sides:

43x - 17x + 4345 = 0

Simplifying:

26x + 4345 = 0

Subtracting 4345 from both sides:

26x = -4345

Dividing both sides by 26:

x = -4345/26

Calculating the value of x:

x ≈ -167.1154

Since distance cannot be negative, we can ignore the negative sign.

Therefore, the total distance is approximately 167.1154 km.

Answer

The total distance is approximately 167.1154 km.