regg can clean a room 3 hours faster than ian. if they can clean a room together in 3 hours, how many hours does regg need to clean the room by himself?

Question

anonymous · Answer

Let Ian can finish work in x hours
Regg can finish it 3 hours faster i.e. x-3 hours
Ian can finish work in x hours
So he can finish 1/x of work in 1 hour
Regg can finish work in x-3 hours
So he can finish 1/(x-3) of work in 1 hour
Together  they can finish 
1/x    +    1/(x-3)       in 1 hour
But they together finish work in 3 hours
So
 3*(1/x    +    1/(x-3) )   = 1
1/x    +    1/(x-3)       =    1/3
Take LCM (LCD)
3x-9+3x=x^2-3x
x^2-9x+9=0
use quadratic formula 
a=1, b=-9, c=9
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