SOLUTION: Maria can sew a dress in 10 hours less time than Stephanie. Together both women can sew a dress in 17 hours. How long would it take if Stephanie works alone?

Question 70389This question is from textbook College Algebra
: Maria can sew a dress in 10 hours less time than Stephanie. Together both women can sew a dress in 17 hours. How long would it take if Stephanie works alone? This question is from textbook College Algebra

Answer by checkley75(3666) (Show Source): You can put this solution on YOUR website!
s*m/(s+m)=17 s=x & m=(x-10
x(x-10)/(x+x-10)=17
(x^2-10x)/(2x-10)=17 now cross multiply
17(2x-10)=x^2-10x
34x-170=x^2-10x
x^2-10x-34x+170=0
x^2-44x+170=0
using the quadratic equation to solve this problem we have
x=(-b+-sqrt[b^2-4ac])/2a
x=(44+-sqrt(-44^2)-4*1*170])/2
x=(44+-sqrt1936-680])/2
x=(44+-sqrt1256)/2
x=44+-35.44)/2
x=79.44/2
x=39.72 hours for Stephanie to sew a dress alone.
39.72-10=29.72 hours for Marie to sew a dress alone.
proof
(39.72*29.72)/(39.72+29.72)=17
1180.5/69.44=17
17=17
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