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# help

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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?

Apr 10, 2020

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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

Apr 10, 2020