Question 1073991
Eduardo's rate is 6 miles per hour.  If he had the 3 mile head start, then for this distance he had run {{{3/6=1/2}}}, half an hour.



<pre>
d is the distance they both go when Jose catches up with Eduardo.
t is how long it takes for Jose to reach Eduardo.

              SPEED     TIME      DISTANCE
JOSE           7.5        t        d
EDUARDO        6         t+1/2     d
</pre>


If solve for time only, t for how long to catchup,
{{{highlight_green(7.5t=6(t+1/2))}}}



-
{{{7.5t=6t+3}}}
{{{1.5t=3}}}
{{{t=3/1.5}}}

{{{highlight(t=2)}}}-----catching-up time 2 hours



RACING DISTANCE d:
-
{{{7.5*2=15}}}
or
{{{6(2+1/2)}}}
{{{12+3}}}
{{{15}}}
-
{{{highlight(d=15)}}}---------   15 mile race