Question

Два гуртожитки знаходяться на одній вулиці на відстані 250 м однин від одного. 100 студентів живуть в першій будівлі, а 150-у другій. Де потрібно побудувати автобусну зупинку, щоб сума усіх відстаней, які проходять студенти від гуртожитків до зупинки, була найменшою

Answer 1

Возле второго общежития так студенты пройдут меньше всего расстояния 25000м

Answer 2

Problem Analysis

We have two dormitories located on the same street, with a distance of 250 meters between them. The first dormitory houses 100 students, while the second dormitory houses 150 students. We need to determine the location to build a bus stop so that the total distance traveled by the students from the dormitories to the bus stop is minimized.

Solution

To minimize the total distance traveled by the students, we should build the bus stop at the midpoint between the two dormitories. This way, the students from both dormitories will have to travel equal distances to reach the bus stop.

The midpoint between two points can be calculated by finding the average of their coordinates. In this case, since the two dormitories are located on the same street, we can simply calculate the midpoint by dividing the total distance between them by 2.

Let's calculate the midpoint and determine the optimal location for the bus stop.

Calculation

The distance between the two dormitories is 250 meters. To find the midpoint, we divide this distance by 2:

Midpoint = 250 meters / 2 = 125 meters

Therefore, the optimal location for the bus stop is 125 meters from the first dormitory and 125 meters from the second dormitory.

Conclusion

To minimize the total distance traveled by the students, the bus stop should be built at a location that is 125 meters from both dormitories.