carcass wrote:
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
Attachment:
RTDfloors.jpg [ 26.98 KiB | Viewed 5891 times ]
Sometimes my ability to write equations for these problems goes AWOL. It did here, initially.
In case others had similar issues, I'm including a good ole RTD chart to clarify my approach.
1. We have rates in seconds and part of a time in minutes. These rates are easy to convert to minutes.
Jan takes 30 seconds per floor to walk down stairs.\(\frac{1 Floor}{30 seconds} = \frac{2 F}{60 secs} = \frac{2 F}{1 min}\),
2 in diagram.
Jan takes 2 seconds per floor to ride the elevator down. \(\frac{1 Floor}{2 seconds} = \frac{30 F}{60 secs} = \frac{30 F}{1 min}\),
30 in diagram
2.
Distance / rate = time (in minutes)
Stairs' time:
\(\frac{x}{2}\)Elevator's time:
\(\frac{x}{30}\)3. We are told that elevator time down + 7 minutes equals walking down the stairs' time, and the rates are in minutes, too, so
\(\frac{x}{30}\) + 7 = \(\frac{x}{2}\) --> (multiply all terms by 30)
x + 210 = 15x
210 = 14x
x = 15
Answer D
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