Question 1006272
Add their rates of working to get
their rate working together
Joseph's rate is:
[ 1 laundry ] / ( 15 min ] = {{{ 1/15 }}}
-----------------------------
Let {{{ t }}} = time in minutes for Mark
and  Joseph to do laundry working together
{{{ 1/t }}} is their rate working together
-----------------------------
Mark's rate when working alone is:
[ 1 laundry ] / [ t + 4  min ] = {{{ 1/( t+4 ) }}}
------------------------------
Add rates of working:
{{{ 1/15 + 1/( t+4 ) = 1/t }}}
Multiply both sides by {{{ 15*t*( t+4 ) }}}
---------------------------------
{{{ t*( t+4 ) + 15t = 15*( t+4 ) }}}
{{{ t^2 + 4t + 15t = 15t + 60 }}}
{{{ t^2 + 4t - 60 = 0 }}}
{{{ ( t + 10 )*( t - 6 ) }}} ( by looking at it )
{{{ t = 6 }}} ( time must be positive )
They can do the laundry together in 6 min
-----------------
check:
{{{ 1/15 + 1/( t+4 ) = 1/t }}}
{{{ 1/15 + 1/(6+4 ) = 1/6 }}}
{{{ 1/15 + 1/10 = 1/6 }}}
{{{ 4/60 + 6/60 = 10/60 }}}
{{{ 10/60 = 10/60 }}}
OK