Question 638939
If Alan does a whole job in 15 days, he will do 1/3 of the job
in 5 days, so 1/3 is done when Bill starts working.
2/3 of the job is left to do.
Now add their rates of working to get their rate working together
In words:
( 1 job ) / ( 15 days ) + ( 1 job ) / ( 20 days ) = ( 2/3 of a job ) / ( x days )
{{{ 1/15 + 1/20 = (2/3) / x }}}
Multiply both sides by {{{ 60x }}}
{{{ 4x + 3x = 120/3 }}}
{{{ 7x = 40 }}}
{{{ x = 5.7143 }}} 
Bill works for 5.7143 days
check:
{{{ 1/15 + 1/20 = (2/3) / x }}}
{{{ .06667 + .05 = .6667 / 5.7143 }}}
{{{ .116667 = .6667 / 5.7143 }}}
{{{ .116667*5.7143 = .6667 }}}
{{{ .666687 = .6667 }}}
close enough