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Manhattan Challenge Problem

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by kakz » Wed Nov 09, 2011 12:42 pm
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 7 flights of stairs and cross the landings between flights, not counting the landings at either end, how long will it take her to climb 10 flights and cross the intervening landings (again not counting landings at either end) at the same rate of travel?
(A)19.0 minutes
(B)19.2 minutes
(C)19.4 minutes
(D)19.6 minutes
(E)19.8 minutes

Please help me with detailed explanations.
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by neelgandham » Wed Nov 09, 2011 1:13 pm
Let the time taken by Josie to climb a flight of stairs be x,
then the time taken by Josie to cross the landing is 2x

If ___ is the landing and | is flight of stairs then the stair-landing looks like this

|___|___|___|___|___|___|

To climb 7 flights of stairs, you need to cross 6 landings.
Time taken by Josie to climb 7 flights of stairs is equal to 7*x = 7x
Time taken by Josie to cross 6 landings is equal to 6*2x = 12x
Total time taken = 12x+7x = 19x = 13.3
19x = 13.3 => 19x = 19*0.7 => x =0.7

To climb 10 flights of stairs, you need to cross 9 landings.
Time taken by Josie to climb 10 flights of stairs is equal to 10*x = 10x
Time taken by Josie to cross the 9 landings is equal to 9*2x = 18x
Total time taken = 10x+18x = 28x = 28*0.7 = 19.6

IMO Answer : D
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by GmatMathPro » Wed Nov 09, 2011 3:04 pm
Good grief, Josie must weigh 500 pounds. Can you imagine taking over 13 minutes to climb seven flights of stairs?

Also, if she takes twice as long to climb a flight of stairs, shouldn't the following be switched?
neelgandham wrote:Let the time taken by Josie to climb a flight of stairs be x,
then the time taken by Josie to cross the landing is 2x
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by user123321 » Wed Nov 09, 2011 3:36 pm
nice one but getting 19.28 or so. but this answer is not among choices.

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by GmatMathPro » Wed Nov 09, 2011 3:53 pm
user123321 wrote:nice one but getting 19.28 or so. but this answer is not among choices.

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Yeah that's what I was getting too.
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by shankar.ashwin » Wed Nov 09, 2011 8:55 pm
Same reasoning as 'neelgandham' but the times reversed,

7*(2x) + 6*(x) = 13.3

x = 0.665

now, 10*(2x) + 9*(x) = 29*x = 19.285 mins (or) 19 mins 17 secs.

Both aren't there in the options though!.
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by neelgandham » Thu Nov 10, 2011 12:29 pm
I stand corrected :) Thanks for letting me know :)
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