Question

20-этажном доме испорчен лифт: он может либо поднять на 13 этажей вверх, либо опу-стить на 8 этажей вниз. За сколько подъёмов и за сколько спусков можно подняться с 7-гоэтажа на 11этаж

Answer 1

Problem Analysis

We have a 20-story building with a malfunctioning elevator that can either go up 13 floors or down 8 floors. We need to determine how many trips it would take to go from the 7th floor to the 11th floor.

Solution

To solve this problem, we need to consider the following: - The elevator can go up 13 floors or down 8 floors in a single trip. - We want to go from the 7th floor to the 11th floor.

Let's break down the steps to find the solution:

1. Determine the direction of travel: - Since we want to go from the 7th floor to the 11th floor, we need to go up. Therefore, we will use the elevator's upward movement.

2. Calculate the number of trips needed to reach the desired floor: - We need to go up 4 floors (from the 7th floor to the 11th floor). - Since the elevator can go up 13 floors in a single trip, we can calculate the number of trips needed by dividing the total number of floors to travel by the number of floors the elevator can cover in one trip. - In this case, 4 floors divided by 13 floors per trip equals approximately 0.31 trips. - Since we cannot have a fraction of a trip, we will round up to the nearest whole number. - Therefore, we will need at least 1 trip to reach the 11th floor.

3. Determine the remaining floors to travel after the last full trip: - After the first trip, we will be on the 11th floor. - We still need to go up 4 floors to reach the desired 11th floor. - Since the elevator can go up 13 floors in a single trip, we can calculate the remaining floors by subtracting the number of floors covered in the previous trips from the total number of floors to travel. - In this case, 4 floors minus 13 floors (covered in the first trip) equals -9 floors. - Since we cannot go down more floors than the elevator can cover in a single trip, we need to switch to the elevator's downward movement.

4. Calculate the number of trips needed for the remaining floors: - We need to go down 9 floors (from the 11th floor to the 7th floor). - Since the elevator can go down 8 floors in a single trip, we can calculate the number of trips needed by dividing the total number of floors to travel by the number of floors the elevator can cover in one trip. - In this case, 9 floors divided by 8 floors per trip equals approximately 1.13 trips. - Since we cannot have a fraction of a trip, we will round up to the nearest whole number. - Therefore, we will need at least 2 trips to reach the 7th floor.

5. Calculate the total number of trips: - We needed 1 trip to go up from the 7th floor to the 11th floor and 2 trips to go down from the 11th floor to the 7th floor. - Therefore, the total number of trips needed to go from the 7th floor to the 11th floor is 1 + 2 = 3 trips.

Answer

To go from the 7th floor to the 11th floor in a 20-story building with a malfunctioning elevator that can either go up 13 floors or down 8 floors, it would take a total of 3 trips. The breakdown of the trips is as follows: - 1 trip going up from the 7th floor to the 11th floor. - 2 trips going down from the 11th floor to the 7th floor.

Please note that this solution assumes that the elevator can only move in the specified increments of 13 floors up or 8 floors down per trip.