Problem from Kaplan Diag. Test

[isisalaska]

Steve goes on the elevator at the 11th floor of a bldg. and rides up at a rate of 57 floors per minute. At the same time Joyce gest on an elevator on the 51st fllor of the same bldg. and rides down at a rate of 63 floor per minute. If they continue traveling at ethese rates, at which floor will they meet?

I need to see the steps...thanks!

[Neo2000]

The difference in floors is 40
Both of them will travel for the same time t
However distance(floors) travelled will be different say X

Time = Distance/Speed

If Time is Constant
D1/S1 = D2/S2

X/(47/60) = (40-X)/(63/60)

Can you simplify from here?

[isisalaska]

thanks
you mean
x/57/60 for S1 right?

[Neo2000]

Nopes. It is given that the person rides up at a speed of 47floors/minute

[isisalaska]

Sorry, it was my fault, I mean 57 instead of 47, thanks!!! I got it now

[jayhawk2001]

Just posting a slightly elaborate version

1 sec rates for each elevator = 57 / 60 and 63 / 60 floors resp.

11 + x * 57/60 = 51 - x * 63/60

x * 120 / 60 = 40

x = 20 sec

So, floor that they will meet = 11 + 20 * 57/60 = floor num 30

[gmatkat]

Diff in floors = 51 - 11 = 40 = Distance
Ratio of rates = 57/63 = 19/21

# of floors travelled from the bottom = part/whole * distance = (19 /(19 + 21)) * 40 = 19

meeting point = 11 + 19 = 30th floor --DONE

[Cybermusings]

I don't know about the elaborate explanations but I tried a very basic trial and error method...here it goes

First Elevator - 57 floors / minute

= 57 floors / 60 seconds

Therefore in one second 57 / 60 = 19 / 20 floors

Second Elevator - 63 floors / minute

= 63 floors / 60 seconds

Therefore in one second 63 / 60 = 21 / 20 floors

After 20 seconds Elevator 1 = 19/20 * 20 = 19 floors up = 11th floor + 19 floors = 30th floor

After 20 seconds Elevator 2 = 21/20 * 20 = 21 floors down = 51-21 = 30th floor

Hence they meet at the 30th floor