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.
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1 and 1/3 hours = 1 + 1/3 = 3/3 + 1/3 = 4/3 hours
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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