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July 28th, 2019, 12:03 AM   #1
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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.
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July 28th, 2019, 04:30 AM   #2
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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.
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July 28th, 2019, 07:24 AM   #3
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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.
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July 28th, 2019, 08:16 AM   #4
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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.
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July 28th, 2019, 11:15 AM   #5
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Quote:
Originally Posted by Ganesh Ujwal View Post
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 View Post
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 View Post
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.
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July 29th, 2019, 03:27 AM   #6
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Quote:
Originally Posted by skipjack View Post
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 View Post
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.
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July 29th, 2019, 05:12 AM   #7
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Quote:
Originally Posted by Ganesh Ujwal View Post
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.

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Originally Posted by Ganesh Ujwal View Post
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.
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July 29th, 2019, 05:19 AM   #8
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Quote:
Originally Posted by skipjack View Post
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?
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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.

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Originally Posted by Ganesh Ujwal View Post
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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