Master and his assistant working together can finish building a room in 15 days. How long would it take each of them to build the room working separately, if it is known that the master can finish it 16 days earlier than the assistant?
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