Posted by **daisy lebron** on Thursday, September 23, 2010 at 5:57am.

a mason can build a wall in 6 hours less than an apprentice. Together they can build the wall in 4 hours. How long would it take the apprentice to build the wall?

- college algebra -
**Reiny**, Thursday, September 23, 2010 at 8:25am
time for apprentice -- x

time for mason -- x-6

rate of apprentice = 1/x

rate of mason = 1/(x-6)

combined rate = 1l/x + 1/(x-6)

= (2x - 6)/(x(x-6))

then

1/[(2x - 6)/(x(x-6))] = 4

x(x-6)/2x-6) = 4

x^2 - 6x = 8x - 24

x^2 - 14x + 24=0

(x-12)(x-2) = 0

x = 12 or x = 2 , the last makes no sense since x-6 would be negative

so x = 12

the apprentice could build the wall in 12 hours

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