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12 May 2008, 10:32
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Lindsey can paint 1/x of a certain room in 20 minutes. What fraction of the same room can Joseph paint in 20 minutes if the two of them can paint the room in an hour, working together at their respective rates?
show your work, solve without picking numbers
A. 1/3x
B. 3x/ x-3
C. x - 3 / 3x
D. x
E. x - 3
show your work, solve without picking numbers
A. 1/3x
B. 3x/ x-3
C. x - 3 / 3x
D. x
E. x - 3
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12 May 2008, 13:56
Kudos
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I get C: ( x-3 / 3x )
Here's how:
Set the equation up as you would any work equation.
( 1 / Lindsay ) + ( 1 / Joseph ) = ( 1 / Total )
Lindsay = 1 / 20x
Joseph = 1 / 20y
Total = 1 hour or 60 minutes
Now solve for Y or the fraction of the room Joseph can paint.
( 1 / 20x ) + ( 1 / 20y ) = ( 1 / 60 )
( 1 / 20y ) = ( 1 / 60 ) - ( 1 / 20x )
( 1 / 20y ) = ( x / 60x ) - ( 3 / 60x )
( 1 / 20y ) = ( x - 3 / 60x )
( 60x / x - 3 ) = 20y
3x / x - 3 = y
Now remeber: the fraction of the room Joseph can paint is 1 / y, so flip the equation and you end up with C.
Here's how:
Set the equation up as you would any work equation.
( 1 / Lindsay ) + ( 1 / Joseph ) = ( 1 / Total )
Lindsay = 1 / 20x
Joseph = 1 / 20y
Total = 1 hour or 60 minutes
Now solve for Y or the fraction of the room Joseph can paint.
( 1 / 20x ) + ( 1 / 20y ) = ( 1 / 60 )
( 1 / 20y ) = ( 1 / 60 ) - ( 1 / 20x )
( 1 / 20y ) = ( x / 60x ) - ( 3 / 60x )
( 1 / 20y ) = ( x - 3 / 60x )
( 60x / x - 3 ) = 20y
3x / x - 3 = y
Now remeber: the fraction of the room Joseph can paint is 1 / y, so flip the equation and you end up with C.
12 May 2008, 14:08
Kudos
Bookmarks
Here's how I solved it...
We know that Lindsey can paint 1/x in 20 minutes, which means she can paint 3/x in 60 minutes. We know that Lindsey + Joseph can paint x/x in 60 minutes, so Joseph can paint (x-3)/x in 60 minutes. To get back down to 20 minutes, just divide Joseph's hourly rate by 3:
(x-3)/(3x) in 20 minutes.
We know that Lindsey can paint 1/x in 20 minutes, which means she can paint 3/x in 60 minutes. We know that Lindsey + Joseph can paint x/x in 60 minutes, so Joseph can paint (x-3)/x in 60 minutes. To get back down to 20 minutes, just divide Joseph's hourly rate by 3:
(x-3)/(3x) in 20 minutes.
