Question 1008201
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/x + 1/y = 1/z}}}


and solve for y


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{{{1/x + 1/y = 1/z}}}


{{{1/8 + 1/y = 1/6}}}


{{{1/8 + 1/y-1/8 = 1/6-1/8}}} Subtract 1/8 from both sides


{{{1/y= 1/6-1/8}}}


{{{1/y= 4/24-3/24}}} Get the denominators equal to the LCD 24


{{{1/y= 1/24}}}


{{{y/1= 24/1}}} 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.