SOLUTION: Rita, Brittany, and Maria can complete a jigsaw puzzle in 1 hour and 30 minutes if they work together. Working alone, it takes Rita 1 less hour to complete the jigsaw puzzle than i

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Question 186778: Rita, Brittany, and Maria can complete a jigsaw puzzle in 1 hour and 30 minutes if they work together. Working alone, it takes Rita 1 less hour to complete the jigsaw puzzle than it takes Brittany, and Brittany completes the jigsaw puzzle three times as fast as Maria. How much time would it take each to complete the jigsaw puzzle working alone

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Which rational function has a graph with the horizontal asymptote Y=-3
Answer by ankor@dixie-net.com(22740) (Show Source):
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Rita, Brittany, and Maria can complete a jigsaw puzzle in 1 hour and 30 minutes
if they work together. Working alone, it takes Rita 1 less hour to complete the
jigsaw puzzle than it takes Brittany, and Brittany completes the jigsaw puzzle
three times as fast as Maria. How much time would it take each to complete the
jigsaw puzzle working alone
:
Let r = time required Rita working alone
Let b = Brittany alone
Let m = Maria alone
Let the completed puzzle = 1
;
+ + = 1
:
"it takes Rita 1 less hour to complete the jigsaw puzzle than it takes Brittany,"
r = (b-1)
;
"Brittany completes the jigsaw puzzle three times as fast as Maria."
m = 3b
:
Substitute for m and r:
+ + = 1
Multiply by 3b(b-1) to get rid of the denominators, results:
3b(1.5) + 3(b-1)*1.5 + 1.5(b-1) = 3b(b-1)
:
4.5b + 4.5b - 4.5 + 1.5b - 1.5 = 3b^2 - 3b
:
10.5b - 6 = 3b^2 - 3b
:
0 = 3b^2 - 3b - 10.5b + 6
A quadratic equation:
3b^2 - 13.5b + 6 = 0
Simplify divide eq by 3
b^2 - 4.5b + 2 = 0
Factors to:
(b-4)(b-.5) = 0
Two solutions
b = .5
b = 4 hrs; this is the only solution that makes sense
then
r = 4 - 1
r = 3 hrs
:
m = 3(4)
m = 12 hrs
;
;
check solution in a calc using the original equation:
+ + =
.5 + .375 + .125 = 1