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guddo
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If machine X works alone at its constant rate, it fills a certain 24 Jan 2024, 09:55
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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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gmatophobia
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If machine X works alone at its constant rate, it fills a certain 24 Jan 2024, 10:39
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guddo
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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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
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If machine X works alone at its constant rate, it fills a certain 25 Jan 2024, 01:13
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guddo
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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2024-01-24_20-52-56.png
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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 )
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If machine X works alone at its constant rate, it fills a certain 24 Jan 2024, 10:35
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guddo
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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2024-01-24_20-52-56.png
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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.
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If machine X works alone at its constant rate, it fills a certain 12 Jun 2024, 08:34
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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
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If machine X works alone at its constant rate, it fills a certain 06 Jul 2024, 09:18
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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
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If machine X works alone at its constant rate, it fills a certain 10 Nov 2024, 20:41
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Bunuel
Quote:
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

Show Spoiler
Attachment:
2024-01-24_20-52-56.png

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.
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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.
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If machine X works alone at its constant rate, it fills a certain 11 Nov 2024, 00:05
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Bunuel
Quote:
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

Show Spoiler
Attachment:
2024-01-24_20-52-56.png

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.
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.
Show more

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%.

17. Work/Rate Problems



For more check below:
ALL YOU NEED FOR QUANT ! ! !
Ultimate GMAT Quantitative MegathreadHope it helps.
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If machine X works alone at its constant rate, it fills a certain 15 Dec 2024, 05:11
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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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