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

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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) About Me  (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) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = Wilma's time to do the job working alone
+t+-+2+ = 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
+1%2Ft+%2B+1%2F%28t-2%29+=+1%2F%284%2F3%29+
+1%2Ft+%2B+1%2F%28t-2%29+=+3%2F4+
Multiply both sides by +t%2A%28t-2%29%2A4+
+4%2A%28t-2%29+%2B+4t+=+3t%2A%28t-2%29+
+4t+-+8+%2B+4t+=+3t%5E2+-+6t+
+3t%5E2+-+14t+%2B+8+=+0+
Use quadratic equation to solve
+t+=+%28-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
+a+=+3+
+b+=+-14+
+c+=+8+
+t+=+%28-%28-14%29+%2B-+sqrt%28+%28-14%29%5E2+-+4%2A3%2A8+%29%29%2F%282%2A3%29+
+t+=+%28+14+%2B-+sqrt%28+196+-+96+%29%29%2F6+
+t+=+%28+14+%2B+sqrt%28100%29+%29%2F+6+
+t+=+%28+14+%2B+10+%29%2F+6+
+t+=+4+
and, also
+t+=+2%2F3+
I can't use +2%2F3+ because I have to subtract 2
and I can't have negative time
+t+=+4+
+t+-+2+=+2+
4 hrs = Wilma's time to do the job working alone
2 = Lilly's time working alone
check answers:
+1%2Ft+%2B+1%2F%28t-2%29+=+3%2F4+
+1%2F4+%2B+1%2F2+=+3%2F4+
+3%2F4+=+3%2F4+
OK