Question 737108
Let {{{ t }}} = time in minutes for Airgle 750 to do the job
{{{ t - 15 }}} = time for A. H. 400 to do job
----------
Add their rate of purifying:
( 1 job ) / ( t min ) + ( 1 job ) / ( t - 15 min ) = 1 / 10 min
{{{ 1/t + 1/( t-15 ) = 1/10 }}}
Multiply both sides by {{{ t*( t-15 )*10 }}}
{{{ 10*( t-15 ) + 10t = t*( t-15 ) }}}
{{{ 10t - 150 + 10t = t^2 - 15t }}}
{{{ t^2 - 35t + 150 = 0 }}}
Use quadratic formula
{{{ t = ( -b +- sqrt( b^2 - 4*a*c )) / (2*a) }}} 
{{{ a = 1 }}}
{{{ b = -35 }}}
{{{ c = 150 }}}
{{{ t = ( -(-35) +- sqrt( (-35)^2 - 4*1*150 )) / (2*1) }}} 
{{{ t = ( 35 +- sqrt( 1225 - 600 )) / 2 }}} 
{{{ t = ( 35 + sqrt( 625 )) / 2 }}} 
{{{ t = ( 35 + 25 ) / 2 }}}
{{{ t = 30 }}}
and, also
{{{ t = ( 35 - 25 ) / 2 }}}
{{{ t = 5 }}} ( reject this solution )
---------
{{{ t - 15 = 15 }}}
It took 30 minutes for Airgle 750 to do the job
It took 15 minutes for A. H. 400 to do job
-------------
check answers:
{{{ 1/t + 1/( t-15 ) = 1/10 }}}
{{{ 1/30 + 1/15 = 1/10 }}}
{{{ 1/30 + 2/30 = 3/30 }}}
{{{ 3/30 = 3/30 }}}
OK