Question 1184255
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One approach is to figure out how much work ONE man does in ONE day (the unit rate of work per person).  Once you know that, the rest falls into place easily.

6 men do the entire job in 8 days

That means 6 men do 1/8 of a job in one day

And one man does  (1/6)*(1/8) = 1/48 job in one day


How much work is done in the first three days?
3days * 6men * (1/48 job/day/man) = 18/48 job 

This leaves (48/48) - (18/48) = 30/48 of the job to do by the remaining 4 men:

Say it takes  N more days...
4 * (1/48) * N =  30/48

N = (30/48) * (48/4) = 7.5 days


Therefore, the entire job takes  3 days + 7.5 days = {{{ highlight(10.5) }}} days.

Check:  3men * 6days * (1/48 job/day/man) + 7.5days * 4men * (1/48 job/day/man) = 48/48 = 1 job (ok)