Algebra, ratios

Question

Painter A can paint a fence in 30 minutes. If painter A and B can paint the fence together in 18 minutes, how long will it take painter B if he painted the fence alone?

Answer 1

Let x = amount of time (in minutes) that it takes painter B to do the job alone

 

1/30 = portion of job done by painter A per minute

 

1/x = portion of job done by painter B per minute

 

1/18 = portion of job done by both painters per minute

 

Then, 1/x + 1/30 = 1/18

 

Multiply by the LCD, 90x, to obtain 90 + 3x = 5x

 

                                                              90 = 2x     x = 45 min

 

Answer 2

It will take him 45 minutes

Reason

1/30+1/45 = 1/18