Advanced Work Rate Word Problem

Question

" A man can lay a concrete sidewalk in 5 days; his assistant can lay the same sidewalk in 8 days. After working together for 2 days, the man is called away. How long will it take the assistant to finish the work? "

     

I am familiar with combined work rate story problems, but I don't quite know how to tackle the one worker leaving the other midway through to finish the job. I've done this problem several different ways and still haven't been able to figure it out.

Answer 1

A man can lay a concrete  sidewalk  in 5 days which means 1/5 sidewalk per day

Similarly, his assistant can lay same sidewalk in 8 days means 1/8 side walk per day.

Both of them working together will complete (1/5+1/8) = 13/40 side walk in a day

Both of them worked together for 2 days and completed 2*13/40 =26/ 40 side walk

After 2 days left over side walk is 1-26/40= 14/40 

Days taken by Assistant to finish left over sidewalk is= (14/40) / (1/8)

                                                                            =( 14*8) / (40*1) = 14/5= 2.8 days

The Assistant will finish leftover sidewalk in 2.8 days