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

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 = x 2 + 16x

0 = x2 + 4x - 96

0 = (x+12) (x-8)

{-12/8}

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