Problem Solving

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.

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

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

Since Steve travels UP from the 11th floor, while Joyce travels DOWN from the 51st floor, the number of floors between Steve and Joyce = 51-11 = 40.

Steve's rate : Joyce's rate = 57:63 = 19:21.
The sum of the parts of this ratio = 19+21 = 40.
Implication:
When Steve and Joyce travel toward each other, of every 40 floors traveled, 19 floors will be traveled by Steve, while 21 floors will be traveled by Joyce.

Since there are a total of 40 floors between Steve and Joyce, Steve travels a total of 19 floors, while Joyce travels a total of 21 floors.
Since Steve travels up 19 floors from the 11th floor, the floor at which the two meet = 11+19 = 30.

The correct answer is C.