Question 948439
r, rate for one worker.
{{{10r*5=1}}}, the one job of THE VINEYARDS GRAPES.
{{{r=1/50}}}.


First hour, {{{1*r*1=(1/50)}}}, a small amount of the job done.

Hour Number Two, two workers, when completed time:
{{{(1/50)*1+(2/50)*1}}}

Hour Number Three, three workers, when completed time:
{{{1/50+2/50+(3/50)*1}}}


UNKNOWN number of hours completed, for finishing harvesting the vineyard's grapes:
(1/50)(1+2+3+...n)=1


1+2+3+...n=50


OR in renderable notational form
{{{sum(x,i=1,n)=50}}}


{{{(n/2)(1+n)=50}}}


{{{n(1+n)=100}}}


{{{n^2+n=100}}}


{{{n^2+n-100=0}}}


{{{n=(-1+- sqrt(1+4*100))/2}}}


{{{n=(-1+sqrt(501))/2}}}

n=10.69, more than ten hours but less than eleven hours.
The actual time from start to finish would be 10 hours 41 minutes.