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Steve gets on the elevator at the 11th floor of a building

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Steve gets on the elevator at the 11th floor of a building

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Steve gets on the elevator at the 11th floor of a building and rides up at a rate of 57 floors per minute. At the same time Joyce gets on an elevator on the 51st floor of the same building and rides down at a rate of 63 floors per minute. If they continue traveling at these rates, at which floor will their paths cross?

A. 19
B. 28
C. 30
D. 32
E. 44

The OA is C.

I am really confuse here. Experts, can you help me? I would appreciate any help you can give me.

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Vincen wrote:
Steve gets on the elevator at the 11th floor of a building and rides up at a rate of 57 floors per minute. At the same time Joyce gets on an elevator on the 51st floor of the same building and rides down at a rate of 63 floors per minute. If they continue traveling at these rates, at which floor will their paths cross?

A. 19
B. 28
C. 30
D. 32
E. 44

The OA is C.

I am really confuse here. Experts, can you help me? I would appreciate any help you can give me.
If Steve is moving at 57 floors/minute and Joyce is moving in the opposite direction at 63 floors/minute, then we know they're moving towards each other at 57+63 = 120 floors/minute.

If they're starting 40 floors apart (51-11) and they're traveling at 120 floors/minute, it will take them 1/3 of a minute to meet. (40/120 = 1/3)

In 1/3 minute, Joyce will have traveled 63 *(1/3) = 21 floors. If she started at the 51st floor, she'll be at the 30th floor (51-21) when they meet. The answer is C

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