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?

The master takes 24 days and the assistant takes 40 days.

Step-by-step explanation:

Let y be the number of days the master takes to build the room and x the number of days the assistant takes.

Ten, working the fraction of the room they can individually build in a day:

1/ x + 1/y = 1/15.

Also  y = x - 16

Substituting for y in the first equation:

1/x + 1/ (x - 16) = 1/15

Multiply through by the LCD  15x(x - 16):

15(x - 16) + 15x =  x(x - 16)

15x + 15x - 240 = x^2 - 16x

x^2 - 16x - 30x + 240 = 0

x^2 - 46x + 240 = 0

(x  - 40)(x - 6) = 0

x = 6, 40.

Now , as y = x - 16 x must be 40, and y =  40 - 16 = 24 days.

So the assistant takes 40 days to build the room and the master takes  24 days.

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