Two elevators move in opposite directions in the same building. David starts at the 11th floor going up at 57 floors per minute, and Albert starts at the 51st floor going down at 63 floors per minute. At which floor do they meet?

Introduction / Context:
This is a relative speed problem on a linear scale (floors). With uniform speeds and opposite directions, the meeting point is found by equating positions as functions of time. Such problems are common in aptitude tests under the topic of time, speed, and distance.

Given Data / Assumptions:

• David: starts at floor 11, moves upward at 57 floors/min.
• Albert: starts at floor 51, moves downward at 63 floors/min.
• They start simultaneously and move uniformly.

Concept / Approach:
Set positions versus time t (in minutes). Meeting occurs when David’s floor equals Albert’s floor. Because they move in opposite directions, their relative speed is the sum of the magnitudes. A simple linear equation suffices.

Step-by-Step Solution:
Let t be minutes after start.David’s floor: F_D = 11 + 57 * t.Albert’s floor: F_A = 51 - 63 * t.At meeting, 11 + 57 * t = 51 - 63 * t.Rearrange: 57 * t + 63 * t = 51 - 11 → 120 * t = 40.Solve: t = 40 / 120 = 1/3 minute.Meeting floor: F = 11 + 57 * (1/3) = 11 + 19 = 30.

Verification / Alternative check:
Relative speed method: distance between them initially = 51 − 11 = 40 floors; combined rate = 57 + 63 = 120 floors/min; time = 40 / 120 = 1/3 min; distance David ascends = 57 * (1/3) = 19 floors; 11 + 19 = 30th floor. Consistent.

Why Other Options Are Wrong:

• 19, 28, 34, 37: Do not satisfy both motion equations at the same time t; plugging t back fails.

Common Pitfalls:

• Using difference of speeds instead of sum for opposite directions.
• Arithmetic errors when solving for t.

Final Answer:
30