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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
(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
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
(x - 4)(x + 1.2) = 0
x = 4 hrs, Matt alone
check solution: (Juan's time = 6 hrs)
.6 + .4 = 1