<PRE><B>Question 543628</B>
How much of a head start did Tim have?
10 AM to 10:30 AM is {{{ .5 }}} hrs
At {{{ 16 }}} mi/hr, Tim goes 
{{{ d[1] = 16*.5 }}}
{{{ d[1] = 8 }}} mi
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Let {{{t}}} = the time it takes for his sister
to catch him.
Let {{{d}}} = the distance she has to travel
Her equation:
(1) {{{ d = 36t }}}
Tim&#39;s equation:
(2) {{{ d - 8 = 16t }}}
Note that they will both trvel for the same
amount of time after Sister leaves and Tim 
has 8 miles less to travel.
Substitute (1) into (2)
(2) {{{ 36t - 8 = 16t }}}
(2) {{{ 20t = 8 }}}
(2) {{{ t = .4 }}} hrs
{{{ .4*60 = 24 }}} min
After 24 minutes she will catch him</PRE>