Question 528667
Add their rate of doing jobs to get
their rate together.
Let {{{t}}} = the time in minutes for the 2nd computer
to finish the job.
Then {{{ t + 21 }}} is the time for the 1st computer 
to do the job
{{{ 1/( t + 21) }}} is the 1st computer's rate
{{{ 1/t }}} is the 2nd computer's rate
{{{ 1/10 }}} is their rate working together
{{{ 1/(t + 21) + 1/t = 1/10 }}}
Multiply both sides by {{{ t*(t + 21)*10 }}}
{{{ 10t + 10*(t + 21) = t*(t + 21) }}}
{{{ 10t + 10t + 210 = t^2 + 21t }}}
{{{ t^2 + t = 210 }}}
Complete the square
{{{ t^2 + t + (1/2)^2 = 210 + (t/2)^2 }}}
{{{ ( t + 1/2 )^2 = 840/4 + 1/4 }}}
{{{ ( t + 1/2)^2 = 841/4 }}}
{{{ ( t + 1/2)^2 = (29/2)^2 }}}
{{{ t + 1/2 = 29/2 }}}
{{{ t = 28/2 }}}
{{{ t = 14 }}} ( ignore the negative square root )
{{{ t + 21 = 35 }}}
It will take the 1st computer 35 min
It will take the 2nd computer 14 min
check:
{{{ 1/(t + 21) + 1/t = 1/10 }}}
{{{ 1/35 + 1/14 = 1/10 }}}
Multiply both sides by {{{ 14*35 }}}
{{{ 14 + 35 = 490/10 }}}
{{{ 49 = 49 }}}
OK