Machines X and Y produce bottles at their respective constant rates.

Question

Machines X and Y produce bottles at their respective constant rates. Machine X produces k bottles in 6 hours and machine Y produces k bottles in 2 hours. How many hours does it take machines X and Y , working simultaneously , to produce 12k bottles?

(A) 8
(B) 12
(C) 15
(D) 18
(E) 24

(A) 8
(B) 12
(C) 15
(D) 18
(E) 24

gurpreetsingh · Accepted Answer

X - k bottle in 6 hours => In 1 hour - k/6 bottles
Y - k bottle in 2 hours => In 1 hour - k/2 bottles

Working together in 1 hour - 2k/3

working together in 3 hours - 2k bottles

2k bottles in 3 hours
=> 2k *6 bottles = 12 bottles in 3*6 = 18 hours

Safiya · Answer

My answer to this question was 8

X -> k bottles in 6 hours -> 1/6
Y -> k bottles in 2 hours -> 1/2

Working together -> 2/3

if they produce k bottles in 2/3 hrs, they will produce 12 * 2/3 bottles in 8 hours.

Could you please point out where I am mistaken??

Safiya · Answer

Ahhh what a silly mistake! Thank you very much gurpreetsingh

parasarora1310 · Answer

X in 6 hours: k bottles
Y in 2 hours: k bottles
Y in 6 hours: 3k bottles

X and Y in 6 hours: 4k bottles

12k bottles: 12/4 = 3 (6 hour periods)
hence 18 hours

muralimba · Answer

try considering the below simple solution.

we have two different time periods resulting in the same quantity of the product (K).

X working for 6 hours, produces K bottles
in those 6 hours Y produces 3K bottles as it produces K in 2 hours.

so in first 6 hours K+3K = 4K
in 12 hours 4K+4k
in 18 hours 4K+4K+4K = 12K

anilnandyala · Answer

Machines X and Y produce bottles at their respective constant rates. Machine X produces k bottles in 6 hours and machine Y produces k bottles in 2 hours. How many hours does it take machines X and Y , working simultaneously , to produce 12k bottles?

(A) 8
(B) 12
(C) 15
(D) 18
(E) 24

formula is work = rate x time

for machine (X) k= r X 6
for machine (Y) k= r X 2
now take a value for k ( for ease which is a multiple of both mac X & y)
take k=12
so rate of machine (x) is 2
so rate of machine (y) is 6

now work is 12k = 12x12 = 144
two machines working siman so rate = 6+2 =8
work = rate X time
144 = 8 X time
so time = 18
so answer D

amitjash · Answer

(6*2/(6+2))*12 = 18

MBAhereIcome · Answer

since the question asks number of HOURS, so we should use this method.

x,y working together to produce k bottles = 6*2/6+2 = 3/2 hrs 
12k bottles = 3*12/2 = 18

shahideh · Answer

\frac{1}{6}+\frac{1}{2}=\frac{1}{T}

T=\frac{3}{2}  for k bottles

and  \frac{3}{2}*12=18  for 12K bottles

Salvetor · Answer

x rate = k/6
y rate = k/2

k/6 + k/2 = 12k / T

solving T = 18

Answer D

EMPOWERgmatRichC · Answer

Hi All,

This is an example of a Work Formula question with a minor 'twist.' The "math" in these questions can be done in a few different ways, but since we have 2 machines working on a task together, without any major "twists" (e.g. one of them stops working at a certain point), we can use the Work Formula:

Work = (A)(B)/(A+B) where A and B are the respective rates of the two machines to do the same task individually.

We're told:
1) Machine X can produce K bottles in 6 hours.
2) Machine Y can produce K bottles in 2 hours.

(6)(2)/(6+2) = 12/8 = 1.5 hours to produce K bottles when working together.

The minor 'twist' is that the question asks how long it takes to produce 12K bottles (not K bottles), so we have to multiply this result by 12...

(1.5 hours)(12) = 18 hours.

Final Answer:  D

GMAT assassins aren't born, they're made,
Rich

cavana · Answer

1) First of all we need to find the rates of each machine:  r*t=w. X: r*6=k, r=\frac{k}{6}; Y: r*2=k, r=\frac{k}{2} 
2) Now we need to combine the two rates:  \frac{k}{6}+\frac{k}{2}=\frac{4k}{6}=\frac{2k}{3} 
3)  \frac{2k}{3}*R=12k, R=12k/\frac{2k}{3}, R=\frac{12k*3}{2k}=18

The correct answer is D.

ScottTargetTestPrep · Answer

We are given that machine X produces k bottles in 6 hours and thus has a rate of k/6. We are also given that machine y produces k bottles in 2 hours and thus has a rate of k/2. We need to determine how many hours it takes machines X and Y to produce 12k bottles when working together. If we let t = the time it takes the two machines working together, we can create the following equation and determine t:

(k/6)t + (k/2)t = 12k

Multiplying the entire equation by 6, we have:

kt + 3kt = 72k

Dividing the entire equation by k, we have:

t + 3t = 72

4t = 72

t = 18 hours

Answer: D

Basshead · Answer

Machine X rate = k/6

Machine Y rate = k/2

Combined rate = 4k/6

Combined, the two machines produce 4k bottles in 6 hours. Therefore they produce 12k bottles in 18 hours. Answer is D.

bumpbot · Answer

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.

Machines X and Y produce bottles at their respective constant rates.

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

Machines X and Y produce bottles at their respective constant rates.

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards