Question 685827
A's rate working alone is {{{ 1/( T + 5 ) }}}
B's rate working alone is {{{ 1/( T + 45 ) }}}
Working together:
{{{ 1/( T+5 ) + 1/( T+45 ) = 1/T }}}
Multiply both sides by {{{ T*( T+5 )*( T + 45 ) }}}
{{{ T*( T + 45 ) + T*( T + 5 ) = ( T+5 )*( T+45 ) }}}
{{{ T^2 + 45T + T^2 + 5T = T^2 + 5T + 45T + 225 }}}
{{{ T^2 = 225 }}}
{{{ T = 15 }}}