Question

Турист проехал восьмую часть пути и ещё 20 км. Если он проедет ещё три четверти оставшегося пути, то до конца останется 16 км. Каков весь путь туриста? Дайте ответ в километрах.

Answer 1

Problem Analysis

We are given that a tourist has traveled one-eighth of the total distance and an additional 20 km. If the tourist travels three-quarters of the remaining distance, there will be 16 km left until the end. We need to determine the total distance traveled by the tourist.

Solution

Let's assume the total distance traveled by the tourist is represented by x km.

According to the given information: - The tourist has traveled one-eighth of the total distance, which is x/8 km. - The tourist has also traveled an additional 20 km.

So, the distance traveled by the tourist before the additional 20 km is x/8 km, and the total distance traveled is x/8 + 20 km.

The remaining distance after traveling three-quarters of the remaining distance is 16 km. Therefore, the remaining distance is (x - (x/8 + 20)) - (3/4)(x - (x/8 + 20)) = 16 km.

Simplifying the equation: (x - x/8 - 20) - (3/4)(x - x/8 - 20) = 16

Now, we can solve this equation to find the value of x.

Calculation

Let's solve the equation to find the value of x.

(x - x/8 - 20) - (3/4)(x - x/8 - 20) = 16

Expanding the equation: (x - x/8 - 20) - (3/4)(x - x/8 - 20) = 16 x - x/8 - 20 - (3/4)(x - x/8 - 20) = 16

Simplifying the equation: x - x/8 - 20 - (3/4)x + (3/32)x + 15 = 16 x - x/8 - (3/4)x + (3/32)x - 20 + 15 = 16

Combining like terms: x - (1/8)x - (9/32)x - 5 = 16

Finding a common denominator: 32x/32 - 4x/32 - 9x/32 - 160/32 - 160/32 = 16

Simplifying the equation: (32x - 4x - 9x - 160 - 160)/32 = 16

Combining like terms: (19x - 320)/32 = 16

Multiplying both sides by 32: 19x - 320 = 16 * 32

Simplifying the equation: 19x - 320 = 512

Adding 320 to both sides: 19x = 512 + 320

Simplifying the equation: 19x = 832

Dividing both sides by 19: x = 832/19

Calculating the value of x: x ≈ 43.79

Answer

The total distance traveled by the tourist is approximately 43.79 km.