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?

Answer 1

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