SOLUTION: working together, matt and juan can restock a store's shelves in 2 hours 24 minutes. alone juan needs two hours longer than matt needs. how long does matt need to restock the shelv

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Question 207992This question is from textbook algebra demystified
: working together, matt and juan can restock a store's shelves in 2 hours 24 minutes. alone juan needs two hours longer than matt needs. how long does matt need to restock the shelves when working alone This question is from textbook algebra demystified

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
working together, matt and juan can restock a store's shelves in 2 hours 24 minutes.
alone juan needs two hours longer than matt needs.
how long does matt need to restock the shelves when working alone
:
Let x = Matt's time working alone
then
(x+2) = Juan's time alone
:
Let the completed job = 1
:
Change 2 hrs 24 min to hrs: 2 hrs & 24/60 = 2.4 hrs
:
2.4%2Fx + 2.4%2F%28%28x%2B2%29%29 = 1
Multiply x(x+2), results:
2.4(x+2) + 2.4x = x(x+2)
:
2.4x + 4.8 + 2.4x = x^2 + 2x
:
4.8x + 4.8 = x^2 + 2x
:
A quadratic equation
0 = x^2 + 2x - 4.8x - 4.8
;
x^2 - 2.8x - 4.8 = 0
Factor
(x - 4)(x + 1.2) = 0
Positive solution
x = 4 hrs, Matt alone
;
:
check solution: (Juan's time = 6 hrs)
2.4%2F4 + 2.4%2F6 =
.6 + .4 = 1