
Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion 
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July 28th, 2019, 12:03 AM  #1 
Senior Member Joined: Aug 2014 From: India Posts: 476 Thanks: 1  how much time Y take to do it alone?
X does half of work that Y does in 1/6 of the time. They take 10 days to complete a work together, how much time Y take to do it alone? Solution: x/y = 2/6 = 1/3 3/4 = 10 3 = 40 Please explain this tiny solution. How are 2/6 & 3/4 obtained? Last edited by skipjack; July 28th, 2019 at 10:48 AM. 
July 28th, 2019, 04:30 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 21,028 Thanks: 2259 
The given solution uses x for the number of days that X alone would need to do the task, and y for the number of days that Y alone would need to do the task. It calculates that x/y = (1/6)/(1/2) = 2/6 = 1/3. It's simpler to say that X can do three times as much as Y in the same time (as (1/2)/(1/6) = 3). Hence when X and Y work together to complete the task, X does 3/4 of the task and Y does 1/4 of the task. Hence the number of days Y working alone needs to complete the task is 10/(1/4) = 40. 
July 28th, 2019, 07:24 AM  #3 
Senior Member Joined: Aug 2014 From: India Posts: 476 Thanks: 1 
What is the meaning of "X does half of work that Y does in 1/6 of the time."? Here 1/6 means what? Why X/Y in the first step? Why not X+Y or X.Y? X does 3/4 of the task and Y does 1/4 of the task.......How you got 4 here? Last edited by skipjack; July 28th, 2019 at 10:50 AM. 
July 28th, 2019, 08:16 AM  #4 
Senior Member Joined: Jun 2019 From: USA Posts: 309 Thanks: 160 
Did you go through any of the prealgebra reviews like I suggested? Until you go back and review very basic equations and word problems, you're just wasting your own time and everyone else's who is trying to help you. 
July 28th, 2019, 11:15 AM  #5  
Global Moderator Joined: Dec 2006 Posts: 21,028 Thanks: 2259  Quote:
That's because the problem effectively tells you that X's work rate is a fixed multiple of Y's work rate. In any specified period of time (such as 10 days), X does 3 times as much work as Y. If Y does 1 unit of work, X does 3 units of work. As a total of (1 + 3) units of work = 4 units of work are done, X does 3/4 of that total amount of work and Y does the remaining 1/4 of it.  
July 29th, 2019, 03:27 AM  #6  
Senior Member Joined: Aug 2014 From: India Posts: 476 Thanks: 1  Quote:
Should I proceed X.Y = 12? Quote:
Basic time & work formulae: M1T1\W1 = M2T2\W2 X(1/6)/(1/2) = y(6)/(1/2) x/y = 36. but you got 1/3. Last edited by skipjack; July 29th, 2019 at 05:13 AM.  
July 29th, 2019, 05:12 AM  #7 
Global Moderator Joined: Dec 2006 Posts: 21,028 Thanks: 2259  If u is a fixed multiple of v, that means that u = c*v, where c is a constant. An equivalent equation is u/v = c. No. It means that if X uses only 1/6 of the time Y uses, X does 1/2 of the work that Y does. 
July 29th, 2019, 05:19 AM  #8 
Senior Member Joined: Aug 2014 From: India Posts: 476 Thanks: 1  
July 29th, 2019, 05:33 AM  #9  
Global Moderator Joined: Dec 2006 Posts: 21,028 Thanks: 2259 
The given solution used x and y to represent the number of days needed by X and Y (respectively) to do the same amount of work. Hence x/y = 1/3 is correct. Equivalently, X's work rate is three times Y's work rate. Quote:
In the above, X's work rate is 1/2 widget per day, whereas Y's work rate is 1/6 widget per day.  

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