Rate-Time-Distance Question

[T]

Jan lives X floors above the ground floor of a highrise building. It takes her 30 seconds per floor to walk down the steps and 2 seconds per floor to ride the elevator. If it takes Jan the same amount of time to walk down the steps to the ground floor as to wait for the elevator for 7 minutes and ride down, then X equals:

A - 4
B - 7
C - 14
D - 15
E - 16

Thanks in advance.

[Guest]

Jan lives X floors above the ground floor of a highrise building. It takes her 30 seconds per floor to walk down the steps and 2 seconds per floor to ride the elevator. If it takes Jan the same amount of time to walk down the steps to the ground floor as to wait for the elevator for 7 minutes and ride down, then X equals:

A - 4
B - 7
C - 14
D - 15
E - 16

Thanks in advance.

My answer will be D. X=15
I used "plug in" number to solve the problem. since 30 seconds per floor ---> walk down, so if x=15, then it would take 30 second * 15 floors= 450 seconds to walk down the steps. 2 seconds per floor ----> ride the elevator, so it will take 2*15=30 seconds + 7 minutes to wait for the elevator (7*60 seconds = 420 seconds) = 450 seconds.
450 sec. walk down = 450 sec. to wait and ride down. Thus, x needs to be 15 in order to have the same number of seconds :)

if you try x=14, 16, 7, or 4, the "walk down" will not equal "to wait and ride down" seconds.

[RonPurewal]

here is perhaps the quickest (and dirtiest) solution.

the overall time must be a multiple of 30 seconds, because it takes 30 seconds to walk down each floor. (that's ridiculously slow - bad knees?) also, the 7 minute wait time is itself a multiple of 30 seconds.
this means that the actual time taken by the elevator must also be a multiple of 30 seconds, because we need to add it to another multiple of 30 seconds (7:00) and get still another multiple of 30 seconds.
the only answer choice that multiplies by 2 seconds to give a multiple of 30 seconds is (d).
done.

[Guest]

Here's the algebra equation:

7 min = 420 seconds.

420 + 2x = 30x

x = 15

[StaceyKoprince]

Thanks, guest!