Question 777950
You have head start of {{{ 1/2 }}} mi
Start a stop watch when the 2nd person is
{{{ 1/2 }}} mi behind.
Let {{{ 1/60 }}} = the time in hours on the stop watch 
when the 2nd person catches the 1st
Let {{{ d }}} = the distance in miles the 2nd person
travels until catching the 1st person
Let {{{ r }}} = the rate in mi/hr of the 2nd person
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1st person's equation:
(1) {{{ d - 1/2 = 45*(1/60) }}}
2nd person's equation:
(2) {{{ d = r*(1/60) }}}
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By substitution,
{{{ r*(1/60) - 1/2 = 45*(1/60) }}}
Multiply both sides by {{{ 60 }}}
{{{ r - 30 = 45 }}}
{{{ r = 75 }}}
The 2nd person must travel 75 mi/hr
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check:
(2) {{{ d = r*(1/60) }}}
(2) {{{ d = 75*(1/60) }}}
(2) {{{ d = 1.25 }}} mi
and
(1) {{{ d - 1/2 = 45*(1/60) }}}
(1) {{{ d = 45/60 + 30/60 }}}
(1) {{{ d = 75/60 }}}
(1) {{{ d = 1.25 }}} mi
OK