its is a combined rate problem when objects are moving towards each other...
so the combined rate would be 57+67 =120 floors per min
= 2 floors per sec
Now find the distance between the floors...
The distance between the two people in floors is
51-11 =40


Now divide 40 by rate i.e. 40/2 =20 sec...
So, the two will meet after 20 secs
After 20 sec steve will be at 11+ 57*20/60 =11+19 = 30 floor
So the answer is C

It can also be solved as follows:
Consider the 2 lifts meet after t min:

11+57t = 51-63t -> t=1/3min

plug t =1/3 to calculate the floor: 11+57/3 = 30

Thanks guys, I guess the hardest part is to set up an equation. From there, its a piece of cake

since we know 57 and 63 are both divisible by 3 we need to look in answer choices that are divisible by 3. it narrow downs to C. so why not start with C.

57 floors in 1 minute then 19 (30-11) floors in 1/3 minute.

63 floors in 1 minute then 21 (51-30) floors in 1/3 minute.

Bingo....they will meet on 30th floor...

nkanakiya wrote:since we know 57 and 63 are both divisible by 3 we need to look in answer choices that are divisible by 3. it narrow downs to C. so why not start with C.

57 floors in 1 minute then 19 (30-11) floors in 1/3 minute.

63 floors in 1 minute then 21 (51-30) floors in 1/3 minute.

Bingo....they will meet on 30th floor...

Checking divisibility of choices is not a good strategy, you would have been better of checking whether the difference bet. starting floor and crossing floor is a factor of speed:

30 - 11 = 19 is a factor of 57
51 - 30 = 21 is a factor of 63

ssmiles08 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

OA: C

if they had the same speed they would meet on the floor exactly in the middle.e. 31st floor. since Joyce's speed is greater, so the floor number must be<31
try options: wherever they meet, they both take the same time to get there.
30: steve travels 19 floors, so time is 19/57=1/3 minutes
Joyce travels 21 floors,time is 21/63=1/3 minutes. so it must be the answer

Steve gets the elevator at 11th floor and rides up @ 57 floors per minute.

Joyce gets on an elevator on the 51st floor of the same building and rides down at a rate of 63 floors per minute

Let "t" be the total time after which they meet.

Floor at which Steve will be after "t" time is...

11+57t.

Floor at which Joyce will be after "t" time is...

63t

Joyce started his journey from 51st floor.. so at the time of contact...

11+57t+63t = 51.

=> t = (1/3).

Hence the floor at which they meet is 11+ 57 * (1/3) = 30.

Hope it is clear...