Elevator Speed

[tryingharder]

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

[d2rockstar]

Originally Posted by tryingharder

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

both are travelling in the opposit direction...net speed is 120 floors per minute

2 floors per second...in 10 seconds both would have travelled 20 floors which is 30th floor for both of them

hence C

[GMAT4LBS]

Steve's Elevator = S, travels at rate of 57 floors per min, so for every second S climbs 57/60 floors =>19/20 floors
Joyce Elevator = J, travels at the rate of 63 floors per min, so for every second J travels 63/60 floors => 21/20 floors

In twenty seconds, S would have climbed 19 floors (30th floor) and J would have traveled 21 floors (30th floor)

[devp]

11 + 57m = 51 - 63m
m = 1/3

So : 11+57m = 30. Hence C.

[abhishek_mumbai]

Yes.. C

[tryingharder]

OA is C

[genius_in_the_gene]

Their relative speed is 57+63 = 120 floors per min.

Distance covered by joyce = 51-11= 40

So time taken = 40/120 = 1/3 rd of a min

so in 1/3rd min, joyce would travel 1/3*63 = 21 floors

answer 51-21 =30

[MBA2010HereWeGo]

Yup agree. However, I was trying to use the formula D=S*T and I was trying to set up the formula. But I don't think that would work since we have only 1 known factor- speed. We also know that time will be the time but that's about how far I got. If anyone knows how to set up the formula, please kindly share. I'd very much like to know how to do so.

[MBAchase]

Yes, the answer should be (C) i.e. 30.

Thanks,
MBAChase

[fm_k]

Yes, you can use the formula : D=S*T
For Steve, D1 = S1*T and for Joyce, D2=S2*T
so D1/S1 = D2/S2 ==> S1/D1 = S2/D2 ==> 57/D1 = 63/D2, then you find the 2 numbers that verify that equality (by decomposing 57 and 63) and you can see that 57/19 = 63/21, so D1=19 and the level is 19+11=30.

Regards