college algebra
posted by daisy lebron .
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?

time for apprentice  x
time for mason  x6
rate of apprentice = 1/x
rate of mason = 1/(x6)
combined rate = 1l/x + 1/(x6)
= (2x  6)/(x(x6))
then
1/[(2x  6)/(x(x6))] = 4
x(x6)/2x6) = 4
x^2  6x = 8x  24
x^2  14x + 24=0
(x12)(x2) = 0
x = 12 or x = 2 , the last makes no sense since x6 would be negative
so x = 12
the apprentice could build the wall in 12 hours