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Seth and Ted can paint a room in 6 hours if they work together. If Ted were to work by himself, it would take him 1 hours longer than it would take Seth working by himself. How long would it take Seth to paint the room by himself if Ted calls in sick

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Answer:

11.5 hours

Step-by-step explanation:

It would take Seith x hours to paint the room by himself, then Ted needs x + 1 hour.

During 1 hour, Seith can do 1/x of the work, Ted can do 1/(x+1) of the work, then we have

1/x + 1/(x + 1) = 1/6

(2x + 1)/[x(x+1)] = 1/6

x(x+1)=6(2x+1)

x^2 + x = 12x + 6

x^2 - 11x - 6 = 0

[tex]x=\frac{11+\sqrt{145}}{2}= 11.5 hours[/tex]

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