SOLUTION: lilly and wilma working together can complete a job in 1 and 1/3 hours. if it takes lilly working alone 2 hours less than wilma to do the job, find the time inquired by each woman

Question 549564: lilly and wilma working together can complete a job in 1 and 1/3 hours. if it takes lilly working alone 2 hours less than wilma to do the job, find the time inquired by each woman working alone.
Found 2 solutions by nerdybill, josmiceli:
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
lilly and wilma working together can complete a job in 1 and 1/3 hours. if it takes lilly working alone 2 hours less than wilma to do the job, find the time inquired by each woman working alone.
.
1 and 1/3 hours = 1 + 1/3 = 3/3 + 1/3 = 4/3 hours
.
Let x = time (hours) it takes Wilma to do the job
then
x-2 = time (hours) it takes Lilly to do the job
.
(4/3)(1/x + 1/(x-2)) = 1
multiplying both sides by 3:
4(1/x + 1/(x-2)) = 3
multiplying both sides by x(x-2):
4((x-2) + x) = 3x(x-2)
4(2x-2) = 3x^2-6x
8x-8 = 3x^2-6x
-8 = 3x^2-14x
0 = 3x^2-14x+8
0 = 3x^2-12x-2x+8
0 = (3x^2-12x)-(2x-8)
0 = 3x(x-4)-2(x-4)
0 = (x-4)(3x-2)
x = {2/3, 4}
We can toss out the 2/3 (extraneous) because it doesn't make sense leaving
x = 4 hours (Wilma)
.
Lilly:
x-2 = 4-2 = 2 hours

Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let = Wilma's time to do the job working alone
= Lilly's time working alone
Add their rates of working to get their
rate working together
( 1 job / t hrs ) + ( 1 job / t-2 hrs ) = rate working together

Multiply both sides by

Use quadratic equation to solve

and, also

I can't use because I have to subtract
and I can't have negative time

4 hrs = Wilma's time to do the job working alone
2 = Lilly's time working alone
check answers:

OK
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