If machine X works alone at its constant rate, it fills a certain

Question

If machine X works alone at its constant rate, it fills a certain production order of bolts in 4 hours. If machine Y works alone at its constant rate, it fills the same production order in 6 hours. If the two machines work simultaneously and independently at their respective constant rates to fill this production order, what fraction of the number of bolts in the order will be made by machine X?

A. 1/3

B. 2/5

C. 5/12

D. 3/5

E. 2/3

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Official Answer

D

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gmatophobia · Accepted Answer

Let's assume that we need to produce 24 bolts.

Number of bolts produced per hour by machine X =  \frac{24}{4} = 6  bolts / hour

Number of bolts produced per hour by machine Y =  \frac{24}{6} = 4  bolts / hour

Hence, both machines together produce 10 bolts per hour.

Time taken to produce 24 bolts = 24/10 hours

Bolts made by machine X = 24/10 * 6

Required Fraction =  \frac{\frac{24*6}{10}}{24} = \frac{3}{5}

Option D

sachi-in · Answer

It's very simple if we consider rate of work each hour: 
Each hour together:
 X does 1/4 th of work => 3/12 th of work
 Y does 1/3 rd of work => 2/12 th of work

So each hour they work together X will do 3 parts Y 2 parts.

Hence X will do 3 / (3 + 2) parts => 3/5 parts ( doesn't matter how long they work together )

Bunuel · Answer

Since machine X needs 4 hours for the same task that machine Y needs 6 hours for, that's 50% more time. Therefore, if x% of the job is done by machine X, then x/1.5 = 2x/3% is done by machine Y. So, we have x + 2x/3 = 100%, which yields x = 60% = 3/5.

Answer: D.

demawtf · Answer

W=R*t

x--> t=4 --> Rx=1/4
y--> t=6 --> Ry=1/6

TOGETHER Rxy=1/4+1/6=5/12 --> it means that together they deliver 5/12 orders per hour

Focusing on x, given that Rx=1/4 let's create the fraction as Rx/Rxy= 1/4 * 12/5 = 12/20 = 3/5

sherifY · Answer

I think a quick way is to identify that i care about the share of X and to plug in numbers
I think an easy way to do it is to find the LCM -> 12. 
At 12 hours X produces 3 bolts 
At 12 hours Y produces 2 bolts 
Share of X = 3/5

Gauri09 · Answer

Hi Bunuel, thank you for the explanation. Can you explain in more detail why you did x/1.5, and how to derive this method intuitively.

Bunuel · Answer

Since machine X takes 4 hours and machine Y takes 6 hours, Y does 1.5 times less work than X in the same time. This means that when working together, if machine X completes x% of the work, then machine Y will complete 1.5 times less, or x/1.5%.

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Tushaar121 · Answer

Let the total number of bolts in the order be N.

Machine X fills the order in 4 hours, so its rate is = N/4 bolts per hour.
Machine Y fills the order in 6 hours, so its rate is = N/6 bolts per hour.

When the two machines work together, their combined rate is: N/4 + N/6.

To add these, first find a common denominator: N/4 + N/6 = (3N/12 + 2N/12) = 5N/12

So, together, they fill 5N/12 bolts per hour.

The fraction of the total number of bolts made by machine X is the ratio of the amount X makes to the total amount: 
= Bolts made by X/Total bolts
= (N/4)/(5N/12)
= 3/5

The fraction of the total number of bolts made by machine X = 3/5.
Option D

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If machine X works alone at its constant rate, it fills a certain

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