It takes Samantha 3 hours more to do a job than it takes Linda. If they work together they can finish the same job in 2 hours. How long will it take Samantha to finish the job alone? Give Samantha's hours, Give Linda's hours, Give the equation, Give the LCD, Give the Restriction, Give the Standard Form, Give the roots, Give the answers.
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Answer:
Samantha = 6
Linda = 3
LCD = 2L (3 + L)
Step-by-step explanation:
So for this problem we can use this formula
1 1 1
——— + ——— = ———
S L T
(Let S = Samantha, L = Linda, and T = time for the two of them)
It was mentioned that it takes 3 more hours for samantha to do the same work as Linda, so we can rewrite it into
1 1 1
——— + ——— = ———
(3 + L) L. T
Why don't we get into solving it?
1 1 1
——— + ——— = ———
(3 + L) L. 2
1 1 1
——— + ——— - ——— = 0
(3 + L) L. 2
2L + 2 (3 + L) - L (3 + L)
———————————— = 0
2L (3 + L)
2L + 6 + 2L - 3L - L²
——————————— = 0
2L (3 + L)
L + 6 - L²
————— = 0
2L (3 + L)
L + 6 - L² = 0
-L² + L + 6 = 0
L² - L - 6 = 0
L² + 2L - 3L - 6 = 0
L ( L + 2) - 3 ( L + 2) =0
(L + 2) (L - 3) = 0
L= -2
L= 3
Checking:
1 1 1
——— + ——— = ———
(3 + 3) 3 2
1 1 1
——— + ——— = ———
6 3 2
1 2 1
——— + ——— = ———
6 6 2
3 1
——— = ———
6 2
1 1
——— = ——— ✓ True
2 2