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Algebra I: Quadratic Problem on Time and Work
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Quadratic Problem on Time and Work

Example: A takes 6 days less than the time taken by B to finish a piece of work. If both A and B together can finish it in 4 days, find the time taken by B to finish the work.
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Solution: Assume B alone takes x days to finish the work. Then, A alone can finish it in (x - 6) days.
(A's one day's work) + (B's one days's work) = 1/x + 1/(x - 6)
(A + B)'s one day's work = 1/4.
    1/x + 1/(x - 6) = 1/4
(x - 6 + x)/[x (x - 6)] = 1/ 4
(2x - 6)/(x2 - 6x) = 1/4
8x - 24 = x2 - 6x
x2 - 14x + 24 = 0
x2 - 12x - 2x + 24 = 0
(x -12) (x - 2) = 0
x = 12 or x = 2.
But x cannot be less than 6. So, x = 12.
Hence, B alone can finish the work in 12 days.
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