Let the number of days that the master can finish the room = D
So he does 1/D of the work in one day
Let the number of days that his assistant takes = D + 16
So he does 1 / ( D + 16) of the work in one day
So in one day we have this equation
1/D + 1 / (D + 16) = 1 / 15
[ D + 16 + D] 1
___________ = ____ cross-multiply
D (D + 16) 15
15 [ D + D + 16] = D (D + 16)
15 [ 2D + 16] = D^2 + 16D
30D + 240 = D^2 + 16D rearrange as
D^2 - 14D - 240 = 0 factor
(D - 24) ( D + 10) = 0
Only the first factor set to 0 and solve gives us our solution of D = 24
It takes the master 24 days to finish the room
It takes the assistant 16 + 24 = 40 days to finish the room