Question 573483
The Mother's head start is:
{{{ 4.5*(1/4) = 1.125 }}} hrs ( or 1 hr 7.5 min )
Now start a stopwatch when Daughter leaves
They will jog for the same amount of time, {{{t}}}, until they meet
Let the distance Daughter jogs until they meet = {{{d}}}
Daughter's equation:
(1) {{{ d = 5t }}}
Mother's equation:
(2) {{{ d - 1.125  = 4.5t }}}
Substitute (1) into (2)
(2) {{{ 5t - 1.125 = 4.5t }}}
(2) {{{ .5t = 1.125 }}}
(2) {{{ t = 1.125/.5 }}}
(2) {{{ t = 2.25 }}}
It will take the Daughter 2 hrs and 15 min to catch her Mother
and, since
(1) {{{ d = 5t }}}
(1) {{{ d = 5*2.25 }}} 
(1) {{{ d = 11.25 }}} mi
They both will have jogged 11.25 mi
check answer:
(2) {{{ d - 1.125  = 4.5t }}}
(2) {{{ 11.25 - 1.125  = 4.5*2.25 }}}
(2) {{{ 10.125 = 10.125 }}}
OK