<PRE><B>Question 775811</B>
1 job = 1 wall.


Look first at the 4 people doing 7 jobs in 31 minutes.  One job would require these four people to only work (1/7) of the 31 minutes.  Meaning is:
4 people do 1 job in (1/7)31 minutes.


WHAT is the one-person rate for 1 job?  Instead of 4 people and {{{(1/7)31}}} minutes, this would be 1 person and 4 times more than {{{(1/7)31}}}.
1 person does at the rate of {{{1/(4*(1/7)31)}}} job per minute.
1 person rate is {{{highlight(7/(4*31))}}} job per minute.


The uniform rate basic idea is r*t=j where r = rate of work in jobs per minute, t is the work time in minutes, and j is how much or many jobs.  Also, the rates of the same kind of persons doing the work are simply added when they work together, ideally; and multiplication is used to show their count.  


Given the one-person rate found, n=10 people to do the work, and j=8 for 8 walls, find t, the number of minutes to paint the 8 walls  (the 8 jobs).


{{{highlight(10(7/(4*31))*t=8)}}}
Solve for t.

{{{t=(8*4*31)/(10*7)}}}
{{{t=(16*31)/(35)}}}
{{{highlight(t=496/35)}}} minutes



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Yes, the whole number part of the quotient IS 14.</PRE>