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# U and T can produce 10,000 units in x hours when working together at t

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Math Revolution GMAT Instructor
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U and T can produce 10,000 units in x hours when working together at t  [#permalink]

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16 Nov 2016, 15:15
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Difficulty:

25% (medium)

Question Stats:

81% (01:37) correct 19% (02:55) wrong based on 260 sessions

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U and T can produce 10,000 units in x hours when working together at their constant rates. If U can produce 10,000 units in 4x/3 hours alone at the constant rate, in how many hours can T produce 10,000 units alone at the constant rate, in terms of x?
A. 5x/2 B. 4x C. 2x D. x E. x/2

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"Only $99 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" ##### Most Helpful Expert Reply CEO Joined: 11 Sep 2015 Posts: 3235 Location: Canada Re: U and T can produce 10,000 units in x hours when working together at t [#permalink] ### Show Tags 17 Nov 2016, 05:55 2 Top Contributor 3 MathRevolution wrote: U and T can produce 10,000 units in x hours when working together at their constant rates. If U can produce 10,000 units in 4x/3 hours alone at the constant rate, in how many hours can T produce 10,000 units alone at the constant rate, in terms of x? A. 5x/2 B. 4x C. 2x D. x E. x/2 For work questions, there are two useful rules to consider: Rule #1: If a person can complete an entire job in k hours, then in one hour, the person can complete 1/k of the job Example: If it takes Sue 5 hours to complete a job, then in one hour, she can complete 1/5 of the job. In other words, her work rate is 1/5 of the job per hour Rule #2: If a person completes a/b of the job in one hour, then it will take b/a hours to complete the entire job Example: If Sam can complete 1/8 of the job in one hour, then it will take him 8/1 hours to complete the job. Likewise, if Joe can complete 2/3 of the job in one hour, then it will take him 3/2 hours to complete the job. Let’s use these rules to solve the question. . . . . . . . For convenience, let's just say that The Entire Job = producing 10,000 units. U and T can produce 10,000 units in x hours when working together at their constant rates. In other words, machines U and T (working together) can complete the entire job in x hours. When we apply Rule #1, we see that, IN ONE HOUR, the machines can complete 1/x of the entire job U can produce 10,000 units in 4x/3 hours alone at the constant rate In other words, machine U (working alone) can complete the entire job in 4x/3 hours. When we apply Rule #1, we see that, IN ONE HOUR, machine U can complete 3/4x of the entire job We'll use the fact that: (Machine U's output in ONE HOUR) + (Machine T's output in ONE HOUR) = (The combined machines' output in ONE HOUR) In other words, 3/4x + (Machine T's output in ONE HOUR) = 1/x So, Machine T's output in ONE HOUR = 1/x - 3/4x = 4/4x - 3/4x = 1/4x In other words, in ONE HOUR machine T can complete 1/4x of the entire job When we apply Rule #2, we see that it takes machine T a total of 4x/1 hours to complete the entire job Answer: RELATED VIDEO _________________ Test confidently with gmatprepnow.com ##### General Discussion Manager Joined: 28 Jun 2016 Posts: 207 Location: Canada Concentration: Operations, Entrepreneurship Re: U and T can produce 10,000 units in x hours when working together at t [#permalink] ### Show Tags 16 Nov 2016, 15:29 MathRevolution wrote: U and T can produce 10,000 units in x hours when working together at their constant rates. If U can produce 10,000 units in 4x/3 hours alone at the constant rate, in how many hours can T produce 10,000 units alone at the constant rate, in terms of x? A. 5x/2 B. 4x C. 2x D. x E. x/2 Assume x=3 Since work done is same. 1/4 + 1/y = 1/3 1/y = 1/12 y has to be written in terms of x. Therefore y = 12 = 4*3 = 4x B Sent from my iPhone using GMAT Club Forum mobile app Board of Directors Status: QA & VA Forum Moderator Joined: 11 Jun 2011 Posts: 4274 Location: India GPA: 3.5 WE: Business Development (Commercial Banking) Re: U and T can produce 10,000 units in x hours when working together at t [#permalink] ### Show Tags 17 Nov 2016, 07:42 2 1 MathRevolution wrote: U and T can produce 10,000 units in x hours when working together at their constant rates. If U can produce 10,000 units in 4x/3 hours alone at the constant rate, in how many hours can T produce 10,000 units alone at the constant rate, in terms of x? A. 5x/2 B. 4x C. 2x D. x E. x/2 $$Efficiency of U + T = \frac{10000}{x}$$ $$Efficiency of U = \frac{30000}{4x}$$ So, Efficiency of T = ( Efficiency of U + T ) - ( Efficiency of U ) Or, Efficiency of T = $$\frac{10000}{x} - \frac{30000}{4x}$$ Or, Efficiency of T = $$\frac{10000}{4x}$$ Time required to produce 10000 units = $$10000/\frac{10000}{4x}$$ = $$4x$$ Hence, correct answer will be (B) 4x _________________ Thanks and Regards Abhishek.... PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only ) Intern Joined: 17 Apr 2016 Posts: 4 Re: U and T can produce 10,000 units in x hours when working together at t [#permalink] ### Show Tags 17 Nov 2016, 09:48 1 Abhishek009 wrote: MathRevolution wrote: U and T can produce 10,000 units in x hours when working together at their constant rates. If U can produce 10,000 units in 4x/3 hours alone at the constant rate, in how many hours can T produce 10,000 units alone at the constant rate, in terms of x? A. 5x/2 B. 4x C. 2x D. x E. x/2 $$Efficiency of U + T = \frac{10000}{x}$$ $$Efficiency of U = \frac{30000}{4x}$$ So, Efficiency of T = ( Efficiency of U + T ) - ( Efficiency of U ) Or, Efficiency of T = $$\frac{10000}{x} - \frac{30000}{4x}$$ Or, Efficiency of T = $$\frac{10000}{4x}$$ Time required to produce 10000 units = $$10000/\frac{10000}{4x}$$ = $$4x$$ Hence, correct answer will be (B) 4x a Sent from my SM-G130H using GMAT Club Forum mobile app Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6625 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: U and T can produce 10,000 units in x hours when working together at t [#permalink] ### Show Tags 18 Nov 2016, 00:33 ==> In case of work rate questions, if it is “together and alone”, you solve it reciprocally. In other words, if you assume the time it takes for T to produce 10,000 units alone as t hrs, you get t=4x from 1/(4x/3)+1/t=1/x. Therefore, B is the answer. Answer: B _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$99 for 3 month Online Course"
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Re: U and T can produce 10,000 units in x hours when working together at t  [#permalink]

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18 Nov 2016, 07:16
1
1
MathRevolution wrote:
U and T can produce 10,000 units in x hours when working together at their constant rates. If U can produce 10,000 units in 4x/3 hours alone at the constant rate, in how many hours can T produce 10,000 units alone at the constant rate, in terms of x?
A. 5x/2 B. 4x C. 2x D. x E. x/2

We are given that U and T can produce 10,000 units in x hours when working together at their constant rates and that U can produce 10,000 units in 4x/3 hours alone at the constant rate.

Thus, we can say the following:

Time for machines U and T = x hours.

Rate for machine U = 10,000/(4x/3) = 30,000/(4x) = 7,500/x

Rate for machine T = 10,000/t (where t = the number of hours machine T takes to complete the job alone).

Since work = rate x time, we can determine the amount of work done by both machines when working together.

Work done by machine U = (7,500/x)(x) = 7,500

Work done by machine T = (10,000/t)(x) = 10,000x/t

We can now use the combined work equation to determine a value for t.

Work (machine U) + Work (machine T) = total work completed

7,500 + 10,000x/t = 10,000

10,000x/t = 2,500

10,000x = 2,500t

10,000x/2,500 = t

4x = t

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Re: U and T can produce 10,000 units in x hours when working together at t  [#permalink]

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27 Jun 2017, 10:22
Total work = rate of U + rate of T

$$\frac{10,000}{x}=\frac{10,000}{4x/3}+\frac{10,000}{T}$$
where we must find value of T in terms of x
On simplifying we get T=4x

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Re: U and T can produce 10,000 units in x hours when working together at t  [#permalink]

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28 Sep 2018, 03:19
Abhishek009 wrote:
MathRevolution wrote:
U and T can produce 10,000 units in x hours when working together at their constant rates. If U can produce 10,000 units in 4x/3 hours alone at the constant rate, in how many hours can T produce 10,000 units alone at the constant rate, in terms of x?

A. 5x/2 B. 4x C. 2x D. x E. x/2

$$Efficiency of U + T = \frac{10000}{x}$$

$$Efficiency of U = \frac{30000}{4x}$$

So, Efficiency of T = ( Efficiency of U + T ) - ( Efficiency of U )

Or, Efficiency of T = $$\frac{10000}{x} - \frac{30000}{4x}$$

Or, Efficiency of T = $$\frac{10000}{4x}$$

Time required to produce 10000 units = $$10000/\frac{10000}{4x}$$ = $$4x$$

Hence, correct answer will be (B) 4x

Hi...quick question:

Efficiency and rate are the same?

regards
Re: U and T can produce 10,000 units in x hours when working together at t &nbs [#permalink] 28 Sep 2018, 03:19
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# U and T can produce 10,000 units in x hours when working together at t

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