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In XYZ Building, a flight of stairs connects each floor to the next, a

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In XYZ Building, a flight of stairs connects each floor to the next, a  [#permalink]

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New post 23 Apr 2015, 04:01
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Question Stats:

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In XYZ Building, a flight of stairs connects each floor to the next, and each flight of stairs is separated from the next flight by a landing. Josie takes twice as long to climb a flight of stairs at a constant rate as she does to cross a landing at another constant rate. If it takes Josie 13.3 minutes to climb 13 flights of stairs and cross the landings between flights, not counting the landings at either end, how long will it take her to climb 27 flights and cross the intervening landings (again not counting landings at either end) at the same rate of travel?

A. 27.6 minutes
B. 27.8 minutes
C. 28.0 minutes
D. 28.2 minutes
E. 28.4 minutes


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In XYZ Building, a flight of stairs connects each floor to the next, a  [#permalink]

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New post 23 Apr 2015, 05:06
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Bunuel wrote:
In XYZ Building, a flight of stairs connects each floor to the next, and each flight of stairs is separated from the next flight by a landing. Josie takes twice as long to climb a flight of stairs at a constant rate as she does to cross a landing at another constant rate. If it takes Josie 13.3 minutes to climb 13 flights of stairs and cross the landings between flights, not counting the landings at either end, how long will it take her to climb 27 flights and cross the intervening landings (again not counting landings at either end) at the same rate of travel?

A. 27.6 minutes
B. 27.8 minutes
C. 28.0 minutes
D. 28.2 minutes
E. 28.4 minutes


Kudos for a correct solution.

Given :
S=2L
13S + 12L = 798

Asked:
27S + 26L= ?

Solution:
S-2L =0 ------------> \(1^{st}\)
13S + 12L = 798 ------------> \(2^{nd}\)

Solving \(1^{st}\) && \(2^{nd}\)
L=21 Secs
S=42 Secs

27S + 26L= 1680 = 28mins .

Answer C
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Re: In XYZ Building, a flight of stairs connects each floor to the next, a  [#permalink]

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New post 23 Apr 2015, 21:28
1
suppose , to climb one flight of stairs = x min and to cross one landing = y min
Given x=2y

According to given data ,
13X+12y=13.3
so , 13x+6x=13.3

so x=13.3/19

now to find ,
27x+26y=27x+13x=40x=40*13.3/19 = 28.0 mints

Answer C
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Re: In XYZ Building, a flight of stairs connects each floor to the next, a  [#permalink]

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New post 24 Apr 2015, 08:55
Time taken to cross one landing = \(t\)
Time taken to cross a flight of stairs = \(2t\)

Time taken to cross \(13\) stairs + \(12\) landings (in between stairs) = \([13\)(\(2t\)) + \(12t]\) = \(38t\) = \(13.3\) mins
Time taken to cross \(27\) stairs + \(26\) landings (in between stairs) = \([27\)(\(2t\)) + \(26t]\) = \(80t\) = \(?\)

\(\frac{80t}{38t}\) = \(\frac{?}{13.3}\) mins

\(?\) = \(\frac{80*13.3}{38}\) = \(28\) mins

Answer C
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Re: In XYZ Building, a flight of stairs connects each floor to the next, a  [#permalink]

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New post 27 Apr 2015, 02:12
Bunuel wrote:
In XYZ Building, a flight of stairs connects each floor to the next, and each flight of stairs is separated from the next flight by a landing. Josie takes twice as long to climb a flight of stairs at a constant rate as she does to cross a landing at another constant rate. If it takes Josie 13.3 minutes to climb 13 flights of stairs and cross the landings between flights, not counting the landings at either end, how long will it take her to climb 27 flights and cross the intervening landings (again not counting landings at either end) at the same rate of travel?

A. 27.6 minutes
B. 27.8 minutes
C. 28.0 minutes
D. 28.2 minutes
E. 28.4 minutes


Kudos for a correct solution.


MANHATTAN GMAT OFFICIAL SOLUTION:

Since it takes Josie twice as long to climb a flight of stairs as it does to cross a landing, let’s start with the smaller time. Let’s take the time to cross 1 landing and call it x. Then the “flight climbing time,” the time to climb 1 flight, is 2x.

Josie takes 13.3 minutes to climb 13 flights of stairs and 13 – 1 = 12 landings between them. (We “subtract one before we’re done” to count the landings between the flights.)

The relationship can now be written:

13.3 = time to climb 13 flights + time to cross 12 landings
13.3 = 13(2x) + 12x
13.3 = 26x + 12x = 38x
x = 13.3/38 = 133/380

380 can be factored easily: 380 = 38 × 10 = 2 × 19 × 2 × 5
133 is tricky; it equals 7 × 19.
So 133/380 reduces (with the 19’s canceling) to 7/20. That’s x.

Now, the quantity we want is the time to climb 27 flights and cross 27 – 1 = 26 landings.

27(2x) + 26x = ?
54x + 26x = ?
80x = ?
80(7/20) = ? Cancel out the 20, leaving 4 × 7 = 28 exactly.

The correct answer is C.
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Re: In XYZ Building, a flight of stairs connects each floor to the next, a  [#permalink]

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Re: In XYZ Building, a flight of stairs connects each floor to the next, a   [#permalink] 26 Nov 2018, 05:03
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