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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. Thanks from Ganesh Ujwal
 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 pre-algebra 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. Thanks from topsquark
July 28th, 2019, 11:15 AM   #5
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Quote:
 Originally Posted by Ganesh Ujwal What is the meaning of "X does half of work that Y does in 1/6 of the time"?
It should have been worded more clearly. It's intended to mean that if Y can do a certain amount of work in a certain period of time, X can do half that amount of work in 1/6 of the time that Y needed (which is equivalent to stating that X can do 3 times Y's amount of work in the same time that Y used).

Quote:
 Originally Posted by Ganesh Ujwal Why X/Y in the first step?
That's because the problem effectively tells you that X's work rate is a fixed multiple of Y's work rate.

Quote:
 Originally Posted by Ganesh Ujwal X does 3/4 of the task and Y does 1/4 of the task.......How you got 4 here?
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
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Quote:
 Originally Posted by skipjack That's because the problem effectively tells you that X's work rate is a fixed multiple of Y's work rate.
Multiple means X.Y not X/Y.

Should I proceed X.Y = 12?

Quote:
 Originally Posted by skipjack X can do half that amount of work in 1/6 of the time that Y needed
Does it mean Y does the work 1/2 in 6 mins so X does the same 1/2 work in 1/6 mins?

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
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Quote:
 Originally Posted by Ganesh Ujwal Multiple means X.Y not X/Y.
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.

Quote:
 Originally Posted by Ganesh Ujwal Does it mean Y does the work 1/2 in 6 mins so X does the same 1/2 work in 1/6 mins?
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
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Quote:
 Originally Posted by skipjack It means that if X uses only 1/6 of the time Y uses, X does 1/2 of the work that Y does.
X does 1/2 of the work that Y does means both are doing same 1/2 unit of work or not?

July 29th, 2019, 05:33 AM   #9
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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:
 Originally Posted by Ganesh Ujwal X does 1/2 of the work that Y does means both are doing same 1/2 unit of work or not?
Not. It means X does half as much work as Y does. Hence if Y takes 12 days to make 2 widgets, X makes 1 widget in 2 days.

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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