Question 851409
{{{x}}}= time for the small printer to do the job alone, in minutes.
{{{1/x}}}= rate of work for the small printer, in jobs per minute.
{{{1/40}}}= rate of work for the big printer, in jobs per minute
{{{10*(1/x+1/40)}}}= work done by both printers in the first 10 minutes.
{{{15*(1/40)}}}= work done by the big printer in the last 15 minutes.
{{{10*(1/x+1/40)+15*(1/40)=1}}}= number of payroll jobs done.
Multiplying both sides of the equal sign by {{{40x}}} we get
{{{10*(40+x)+15x=40x}}}
{{{400+10x+15x=40x}}}
{{{400+25x=40x}}}
{{{400=40x-25x}}}
{{{400=15x}}
{{{400/15=x}}}
{{{highlight(x=80/3)}}}