OpenStudy user A joined OpenStudy 6 months before OpenStudy user B. After how many months will OpenStudy user B's time spent in OpenStudy be half of OpenStudy user A's time spent in OpenStudy?

Question

parthkohli · Answer

Take user A as $x + 6$, and user B as $x$.

lgbasallote · Answer

so then it will be x + m = (x + 6 + m)/2?

parthkohli · Answer

Though I did this through trial and error and got 6 months as the answer =))

lgbasallote · Answer

where m is months later of course

lgbasallote · Answer

lol what's the algebraic solution?

parthkohli · Answer

Thinking :p

lgbasallote · Answer

i think my equation makes sense :/

parthkohli · Answer

$ \color{Black}{\Rightarrow 2x = (x + 6) + 6 }$
Aha

parthkohli · Answer

Solve for $x$.

parthkohli · Answer

$2x = x + 12$

$ \color{Black}{\Rightarrow x = 12 }$

wait :/

lgbasallote · Answer

why +6?

parthkohli · Answer

Well, if we say that the answer is 'after x months', then the time spent for the newbie would be x months and the other one x + 6 months

lgbasallote · Answer

2(x+m) = x + 6 + m

x + m = 6

therefore 6 months?

parthkohli · Answer

Oh yeah we could make a system :P

parthkohli · Answer

Correct

lgbasallote · Answer

thanks

parthkohli · Answer

Lol you did the problem on your own =))

lgbasallote · Answer

a follow up question was asking what if A came 11 months before B?

parthkohli · Answer

Where are these questions, seriously :P

lgbasallote · Answer

the answer's not in my book =_=

lgbasallote · Answer

my book?

parthkohli · Answer

Your book knows OS lol

lgbasallote · Answer

yup :p i wrote it ^_^

parthkohli · Answer

lol

lgbasallote · Answer

so what if 11 months?

parthkohli · Answer

$ \color{Black}{\Rightarrow x + m = 11 }$

$ \color{Black}{\Rightarrow 2(x  + m) = x +11 + m }$

lgbasallote · Answer

so x + m = 11...

lgbasallote · Answer

that's weird..

parthkohli · Answer

$ \color{Black}{\Rightarrow 22 = 11 + 11 }$

$ \color{Black}{\Rightarrow 22 = 22 }$

:/

lgbasallote · Answer

the time difference between them is the amount of time it takeS B to be half of A?

parthkohli · Answer

lol I'm noticing something here

parthkohli · Answer

If x + m = 6, then it takes 6 months
If x + m = 11, then it takes 11 months

parthkohli · Answer

I am a magician =.=

lgbasallote · Answer

something is definitely weird >.<

lgbasallote · Answer

let's say i joined July and you joined april...that means 9 months after april i should be double of you..

oh yeah makes sense lol

parthkohli · Answer

lol that's easy xP

parthkohli · Answer

See what we proved with trial and error mwahahaha

lgbasallote · Answer

lol

parthkohli · Answer

TRIAL AND ERROR FTW