Question 947348
Uniform Rates for Doing a Job.
{{{(rate)(time)=(job)}}}


If n agents which work at the same rate of r do a job, the rate is n*r.



{{{M*r*1=J}}}, the condition.


Let t be how many days for the M-5 men.
{{{(M-5)*r*t=K}}}.


The system is
{{{system(Mr*1=J,(M-5)rt=K)}}}
and the unknown variables are r and t.
The question is, how many more days is t than 1, but you essentially want to solve for t.


First equation gives you {{{r=J/M}}}.
Substitute into the second equation.
{{{(M-5)(J/M)*t=K}}}


{{{t=K(M/J)(1/(M-5))}}}


{{{highlight(t=(KM)/(J(M-5)))}}}, or you could perform the indicated multiplication in the denominator.  Finish by subtracting 1.  "How many more day...?"