Question

One crew can frame a single story house in 7 days, while a second crew can do it in 5 days. how long will it take to frame a single house if the second crew arrived 2 days after the first.

Im having problems setting it up with the 2 days after the first

Answer 1

Let the completed job be represented by 1
The first crew worked for 2 days, so they did 2/7 of the job.

This leaves 5/7 of the job to be finished by the combined work of the two crews

rate of first crew = 1/7
rate of 2nd crew = 1/5
combined rate = 1/7 + 1/5 = 12/35

let the time remaining for the job to be done be t
(12/35) t = 5/7
t = 5/7 * 35/12 = 25/12 hrs
= 2 hours and 5 minutes

check:
2(1/7) + (25/12)(12/35)
= 2/7 + 5/7
= 1 , the job is done