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

Question

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.

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

Lucky2783 · Answer

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

adityadon · Answer

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

sudh · Answer

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

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

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

Answer C

Bunuel · Answer

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.

Fdambro294 · Answer

Assuming the Speed stays Constant across both Scenarios and the Landings/Flights of Stairs remain the Same Distance:

Since we are NOT Counting either Landings at the beginning or end:

If there is N Flights
There will be (N-1) Landing

Ratio of:

Time to travel 1 Flight : Time to Travel 1 Landing = 2x : 1x

Time to travel 13 Flights: Time to Travel 12 Landings = 13x : 6x

Total Time = 13.3 min = 13x + 16x

13.3 = 19x

x = .7

Total Time to Travel 13 Flights = 13 * .7 = 9.1 minutes

Total Time to Travel 12 Landings = 12 * .7 = 4.2 minutes

Speed on Flights = 13/9.1 flights per min.

Speed on Landings = 12/4.2 landings per min.

To cover 27 Flights, there would be 26 landings.

Time to Cover 27 Flights = 27 Flights / Speed on Flights = (27/1) / (13/9.1) = 245.7/13 =

18.9 minutes

Time to Cover 26 Landings = 26 Landings / Speed on Landings = (26/1) / (12/4.2) = 109.2 / 12 =

9.1 minutes

Answer:

Total Time = 18.9 + 9.1 = 28.0 minutes

Answer - C-

IanStewart · Answer

Climbing a flight of stairs is like crossing 2 landings. The question tells us it takes 13.3 minutes to climb 13 flights and cross 12 landings, so it takes 13.3 minutes to cross 2*13 + 12 = 38 landings. We then want to know how long it will take to climb 27 flights and cross 26 landings, which is like crossing 2*27 + 26 = 80 landings. At the same speed it will take 80/38 times as long to travel 80/38 times as far, so the answer is (80/38)*13.3 = 4*133/19 = 4*7 = 28.

BAA5 · Answer

Let time per landing be x, time per flight of stairs = 2x,
13 flights of stairs imply 26x for flight+ 12x (12 landings between 13 flights)=> 38x= 13.3 min, x= 13.3/38

27 flights mean 54x+ 26x (26 landings between 27 flights) = 80x= 80*13.3/38 = 28 minutes

bumpbot · Answer

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