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David gets on the elevator at the 11th floor of a building and rides up at the rate of 57 floors per minute. At the same time, Albert gets on an elevator at the 51st floor of the same building and rides down at the rate of 63 floors per minute. If they continue travelling at these rates, then at which floor will their paths cross ?
  • a)
    19
  • b)
    28
  • c)
    30
  • d)
    37
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
David gets on the elevator at the 11thfloor of a building and rides up...
Suppose their paths cross after x minutes.
Then, 11 + 57x = 51 - 63x    ⇔    120x = 40
x =1/3
Number of floors covered by David in (1/3) min. =((1/3)x 57)= 19
So, their paths cross at (11+19) i.e., 30th floor.
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Most Upvoted Answer
David gets on the elevator at the 11thfloor of a building and rides up...
Let's analyze the problem step by step:

1. Determine the relative distance between David and Albert:
- David starts at the 11th floor and goes up at a rate of 57 floors per minute.
- Albert starts at the 51st floor and goes down at a rate of 63 floors per minute.

To find the relative distance between them, we need to subtract their initial positions:
Relative distance = 51 - 11 = 40 floors

2. Calculate the relative speed:
- David's rate is 57 floors per minute.
- Albert's rate is 63 floors per minute.

To find the relative speed, we need to subtract their rates:
Relative speed = 63 - 57 = 6 floors per minute

3. Determine the time it takes for their paths to cross:
To find the time it takes for their paths to cross, we divide the relative distance by the relative speed:
Time = Relative distance / Relative speed = 40 floors / 6 floors per minute = 6.67 minutes

4. Calculate the floor at which their paths cross:
Since David starts at the 11th floor and travels for 6.67 minutes at a rate of 57 floors per minute, we can calculate his final floor:
David's final floor = 11 + (6.67 * 57) = 11 + 380.19 = 391.19

Since Albert starts at the 51st floor and travels for 6.67 minutes at a rate of 63 floors per minute, we can calculate his final floor:
Albert's final floor = 51 - (6.67 * 63) = 51 - 421.21 = -370.21

As we can see, David's final floor is positive, indicating an upward movement, while Albert's final floor is negative, indicating a downward movement. Therefore, their paths cross between the 391st and 370th floors.

The only option within this range is option C) 30. Therefore, the correct answer is option C) 30.
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