Question 934502
Part of solving this one is to be able to recognize that it is a UNIFORM RATES problem.  It takes the form of R*T=J for rate, time, job.  The rate also depends on how many agents are participating to do any part of the job.


Assume all men work individually at an equal rate, calling this rate r, in units of JOBS PER DAYS.  The 1 job is "a piece of work".  The men being described will in the way they are distributed, complete ONE job.


"If 6 men can do a piece of work in 14 days, how many men are needed to do the work in 21 days?"


Let r be the rate for one man.
Let n be the unknown number of men to find.
Let j be 1 for ONE WHOLE JOB.
Uniform rates rule here would be of the form, R*t=j, where R depends on the number of men, workers, or agents doing any quantity of job.


{{{highlight((6r)*14=1=(n*r)*21)}}}
That should now make sense.  
Solve for n.




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{{{highlight(6r*14=n*r*21)}}}
{{{(6*14*r)/(r*21)=n}}}
{{{n=(6*14)/21}}}
{{{n=(6*2*7)/(3*7)}}}
{{{n=2*2}}}
{{{highlight(n=4)}}}