Question

a graphic designer and her assistant working together can complete an advertising layout in 6 days. The assistant working alone could complete the job in 16 more days than the designer working alone. How long would it take each person to do the job alone

Answer 1

X= hours needed by the designer 
x+ 16= hours needed by the assistant 

In 6 hours the designer does 6/x of the job 
In 6 hours the assistant does 6/(x + 16) of the job
Together they complete the 1 job


6/x+ 6/( x+16)= 1
6(x+16) +6x =+ x2 16x
6x+ 96+ 6x= x2+ 16x 
0= x2+ 4x- 96 
0= (x+12)(x-8)
{-12/8}

The designer needs 8 hours and the assistant needs 24 hours.