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Jan lives x floors above the ground floor of a highrise building. It t

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Jan lives x floors above the ground floor of a highrise building. It t  [#permalink]

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23 May 2017, 14:09
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Question Stats:

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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

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Concentration: Technology, Strategy
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Re: Jan lives x floors above the ground floor of a highrise building. It t  [#permalink]

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23 May 2017, 15:06
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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

Jan lives x floors above the ground floor.
Jan takes 30 seconds per floor to walk.
Time taken by Jan to reach x floors walking = 30x seconds

Jan takes 2 seconds per floor to ride the elevator. Jan has to wait for 7 mins (7 x 60 = 420 seconds) for elevator.
Time taken by Jan to reach x floors in elevator = 2x + 420 seconds

2x + 420 = 30x
28x = 420
x = 15
Therefore Jan lives on 15 floor. Answer D...
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Re: Jan lives x floors above the ground floor of a highrise building. It t  [#permalink]

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23 May 2017, 19:19
30 secs to walk down each floor. So 30*x seconds to walk down x floors.
2 seconds to ride down each floor. So 2*x seconds to ride down x floors.

It is given that total time to walk down = 7*60 + total time to ride down x floors
Therefore 30*x= 7*60+2*x

30*x-2*x= 7*60
28*x=7*60
x= 7*60/28 = 15
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Jan lives x floors above the ground floor of a highrise building. It t  [#permalink]

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23 May 2017, 20:38
Quickest way without algebra.

7 min = 420 sec.

As per the condition .

steps time = elevator time + 420 sec.

Hence ans choice will definitely be > 420 sec

Now scanning answer choices. We can eliminate A, B and C

A) 4 = 4 * 30 = 120 sec

B) 7 = 7* 30 = 210 sec

C) 14 = 14 * 30 = 420 sec

D) 15 = 15 * 30 = 450 sec

E) 16 = 480 sec

Check condition for option D and E

Option D : 15 * 30 = 15* 2 + 420
=> $$450 = 450$$

Option E: 16 * 30 = 16 * 2 + 420
=> $$480\neq{452}$$
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Re: Jan lives x floors above the ground floor of a highrise building. It t  [#permalink]

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23 May 2017, 22:11
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

x*(1/2)=7+x*(1/30)
x=15
D
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Joined: 22 May 2016
Posts: 2204
Re: Jan lives x floors above the ground floor of a highrise building. It t  [#permalink]

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03 Jun 2017, 12:27
1
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 3117 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

Intern
Joined: 11 Sep 2013
Posts: 21
Schools: CBS '19
Re: Jan lives x floors above the ground floor of a highrise building. It t  [#permalink]

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06 Aug 2018, 09:48
x=?

Given:
Walk down = 30x
Ride down = 2x

Condition:
30x=2x+7min

Solution:
First 7 Min. = 420 Sec.
Then:
30x=2x+420
28x=420
x=420/28
x= 15

(D) 15
CEO
Joined: 11 Sep 2015
Posts: 3234
Re: Jan lives x floors above the ground floor of a highrise building. It t  [#permalink]

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01 Oct 2018, 12:50
Top Contributor
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

Let's first convert 7 minutes to SECONDS in order to have uniform units of measurement.
7 minutes = 420 seconds

Jan's travel time (in seconds) WALKING down = Jan's travel time (in seconds) via ELEVATOR + 420 seconds

It takes her 30 seconds per floor to walk down the steps and 2 seconds per floor to ride the elevator.
There are x floors
So, WALKING time (in seconds) = 30x
And ELEVATOR time (in seconds) = 2x

Plug values into word equation to get: 30x = 2x + 420
Subtract 2x from both sides to get: 28x = 420
Solve: x = 420/28
= 60/4
= 15

Cheers,
Brent
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Re: Jan lives x floors above the ground floor of a highrise building. It t  [#permalink]

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01 Oct 2018, 21:37
Hi All,

We're told that Jan lives X floors above the ground floor of a high-rise building; it takes her 30 SECONDS per floor to walk down the steps and 2 SECONDS per floor to ride the elevator. We're asked 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 which of the following numbers. This question can be solved in a couple of different ways, including by TESTing THE ANSWERS.

To start, there's a significant difference in time between walking and riding the elevator (30 seconds/floor vs. 2 seconds/floor); in the time it takes Jan to walk 1 floor, she can ride the elevator down 15 floors. Given the 5 answer choices, the correct answer will likely be one of the larger options. Let's TEST Answer D first...

IF... Jan travels 15 floors, then
the walking time would be (15)(1/2 minute) = 7.5 minutes
the elevator time would be (15)(2 seconds) = 30 seconds = 1/2 minute
The difference in these two times is 7 minutes, which is an exact match for what we were told. Thus, this must be the answer.

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Re: Jan lives x floors above the ground floor of a highrise building. It t  [#permalink]

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03 Oct 2018, 16:36
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

Since 7 minutes = 420 seconds, we can create the equation:

Jan’s time to walk = Jan’s time to ride

30x = 420 + 2x

28x = 420

x = 15

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Re: Jan lives x floors above the ground floor of a highrise building. It t &nbs [#permalink] 03 Oct 2018, 16:36
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