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Please solve this RATE problem

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Please solve this RATE problem [#permalink] New post 19 Mar 2007, 09:11
Hello,

Please help to solve this problem

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
Senior Manager
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 [#permalink] New post 19 Mar 2007, 10:03
Answer C

They both started same time so they would have travelled same amount of time when they meet.
Let that time be T
Also they together would have travelled 51 -11 = 40 floors

so 57*T + 63*T = 40
solving we get T = 3
Substituting for Steve 57*T = 19
Therfore they meet at 11+19 = 30th Floor
Director
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 [#permalink] New post 19 Mar 2007, 12:40
another way to look at it :

for any problem, when its asked about two objects travelling at different rates meeting/crossing the path - its easier to assume one
of the objects to be stationary

here A - 57 floors/min
B - 63 floors/min

so lets assume A is stationary,

so relative speed of B = 63 + 57 = 120 floors/min

now, the distance = 51-11 = 40

120 x T = 40 => T = 1/3

now, the actual distance (floors) travelled by B in time 1/3 => 63 x 1/3 => 21

so the floor where B will meet A = 51 - 21 = 30 !


PS: in case of problems where objects are travelling in the same direction (how long A takes to catch up with B) just subtract the rates :)
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Thanks [#permalink] New post 19 Mar 2007, 17:24
Thanks so much for solution, I can't believe it was this mind-boggling, seems so easy now!
Thanks   [#permalink] 19 Mar 2007, 17:24
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