Solve the problem

Question

Pat and Mike working together can assemble a bookcase in 6 minutes. It takes Mike, working by himself, 9 minutes longer than it takes Pat working by himself to assemble the bookcase. How long does it take each, working alone, to do the job?

Answer 1

It's helpful to think of work problems in terms of work completed per unit time, rather than time required to complete the job.

 

Pat can finish the job in "p" minutes, so he can finish 1/p of the job in one minute.

 

Mike can finish the job in "p+9" minutes, so he can finish 1/(p+9) of the job in one minute.

 

Together they can finish the job in 6 minutes, so they can finish 1/6 of the job in one minute.

1/p + 1/(p+9) = 1/6

Common denominator is p*(p+9)*6

6*(p+9) + 6p = p*(p+9)

6p + 54 + 6p = p^2 + 9p

p^2 - 3p - 54 = 0

Factor.  (p-9)(p+6)

So p = 9 and p = -6.  Disregard -6.

If p = 9, then 1/9 + 1/18 = 1/6.  This checks out.

So Pat can finish the job in 9 minutes and Mike can finish the job in 18 minutes.