Elevator problem

[gmarino74]

Ok I hope someone can help me with this problem, I know is a rate problem but I just can't find a quick way to solve it:

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 Joy gets on the 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 their paths cross?

A 19
B 28
C 30
D 32
E 44

[nino.kanchaveli]

[quote="gmarino74"]Ok I hope someone can help me with this problem, I know is a rate problem but I just can't find a quick way to solve it:

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 Joy gets on the 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 their paths cross?

A 19
B 28
C 30
D 32
E 44[/A
is the answer A ?
]

[lavishpariyani]

they are going to meetat 30th floor
because time=distance b/w them/(relativespeed) = 1/3 minute
57*1/3=19
hence 30 the floor

[gmarino74]

I am not sure I am convinced by your explanation

[amin.ebadi]

Try this:

D = distance between the starting points = 51-11 = 40 floors
(1) d1 + d2 = D = 40, where d1 is the distance between the meeting point and the starting point of the 1st elevator, and d2 is the distance between the meeting point and the 2nd elevator's starting point.

(2) d1 = v1 * t
(3) d2 = v2 * t

Combine (1) (2) (3) and you end up with t = 1/3
The meeting point P = 11 + t*v1 or P = 51 - v2 * t
In both cases, you get P = 30th floor

Ok?

[gmarino74]

got it. Thank you!

[Ben Ku]

Amin's solution is good. Let me know if there are any additional questions about this problem.

[ms]

Thanks guys.
I guess the key to solving this problem is to remember that it is the time taken by the two elevators before they reach the meeting point is the same. Not the distance. Cheers

[esledge]

Great point, ms. They start at different floors and end at the same floor, so the distance would have to be different. Other key words are "at the same time..."