Work equals rate times time problem

Question

If it takes one person 30 minutes to paint a wall and another person 45 minutes to paint the wall, how long does it take if they are working together?

Answer 1

Let x = number of minutes that it takes to do the job if                     they both work together

 

1/30 = portion of the wall painted by the first painter in                  one minute

1/45 = portion of the wall painted by the second painter                in one minute

1/x = portion of the wall painted per minute if they work              together             

 

1/30 + 1/45 = 1/x

 

Multiply through by the LCD, 90x:

 

3x + 2x = 90

 

5x = 90

 

x = 18 minutes