How long does it take each worker to complete the job alone?

Question

a graphic designer and her assistant working together complete an advertising layout in 6 days. The assistant working alone can complete the job in 16 more days than the designer. How long does 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

12x + 96 = x² + 16x

0 = x² + 4x - 96

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

 

{-12, 8}

 

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