Question

Решите задачу рациональным способом. До обеда турист прошел половину намеченного пути. Когда после обеда он прошел 2/3 оставшегося пути, ему осталось пройти 4 км. Какова протяженность намеченного туристом пути?

Answer 1

1- 2/3 =1/3 пути, или 4км, тогда
оставшийся путь после обеда =
4:1*3=12 км или пол пути
12*2=24 км весь путь

Answer 2

Problem Analysis

To solve this problem, we need to find the total distance of the tourist's planned route. We are given that the tourist walked half of the planned distance before lunch and then walked two-thirds of the remaining distance after lunch, leaving 4 km to be covered. Let's assume the total distance of the planned route is D km.

Solution

1. Before lunch, the tourist walked half of the planned distance, which is D/2 km. 2. After lunch, the tourist walked two-thirds of the remaining distance, which is (D - D/2) * (2/3) km. 3. The remaining distance after lunch is 4 km. 4. We can set up the equation: (D - D/2) * (2/3) = 4. 5. To solve for D, we can simplify the equation: - Multiply both sides by 3/2: (D - D/2) * 2 = 4 * (3/2). - Simplify: 2D - D = 6. - Combine like terms: D = 6.

Answer

The total distance of the tourist's planned route is 6 km.

Verification

Let's verify the solution by substituting the value of D back into the equation: - Before lunch, the tourist walked half of the planned distance: 6/2 = 3 km. - After lunch, the tourist walked two-thirds of the remaining distance: (6 - 3) * (2/3) = 2 km. - The remaining distance after lunch is 4 km, which matches the given information.

Therefore, the solution is correct.