Question 770912
Let {{{ R[b] }}} = B's rate of working
{{{ 1.3*R[b] }}} = A's rate of working
---------------
Also given is:
A's rate of working is ( 1 job ) / ( 23 days ) 
{{{ 1.3*R[b] = 1/23 }}}
{{{ R[b] = 1/29.9 }}}
and
{{{ R[a] = 1/23 }}}
----------------
Let {{{ t }}} = time in days to finish 
job working together
{{{ R[a] + r[b] = 1/t }}}
{{{ 1/23 + 1/29.9 = 1/t }}}
Multiply both sides by {{{ 23*29.9*t }}}
{{{ 29.9t + 23t = 23*29.9 }}}
{{{ 52.9t = 687.7 }}}
{{{ t = 13 }}}
Working together, they can do the
job in 13 days
check:
{{{ 1/23 + 1/29.9 = 1/13 }}}
{{{ .04348 + .03344 = .07692 }}}
{{{ .07692 = .07692 }}}
OK