SOLUTION: ryan can paint a room in 8 hours when working alone. if stephanie helps him, the total job takes 6 hours. how long does it take stephanie if she works alone

Algebra ->  Rate-of-work-word-problems -> SOLUTION: ryan can paint a room in 8 hours when working alone. if stephanie helps him, the total job takes 6 hours. how long does it take stephanie if she works alone      Log On


   

Question 1008201: ryan can paint a room in 8 hours when working alone. if stephanie helps him, the total job takes 6 hours. how long does it take stephanie if she works alone
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let
x = time it takes for Ryan to do the job alone
y = time it takes for Stephanie to do the job alone
z = time it takes if they worked together

In this case,
x = 8
y = unknown
z = 6

x,y,z are time values in hours

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We'll use this formula

1%2Fx+%2B+1%2Fy+=+1%2Fz

and solve for y

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1%2Fx+%2B+1%2Fy+=+1%2Fz

1%2F8+%2B+1%2Fy+=+1%2F6

1%2F8+%2B+1%2Fy-1%2F8+=+1%2F6-1%2F8 Subtract 1/8 from both sides

1%2Fy=+1%2F6-1%2F8

1%2Fy=+4%2F24-3%2F24 Get the denominators equal to the LCD 24

1%2Fy=+1%2F24

y%2F1=+24%2F1 Take the reciprocal of both sides

y=+24

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It will take Stephanie 24 hours to do the job if she did the job alone.