<PRE><B>Question 206771</B>
A woman begins jogging at 3:00 P.M., running due north at a 6- minute- mile pace. Later, she reverses direction and runs due south at a 7- minute mile pace. If she returns to her starting point at 3:45 P.M., find the total number of miles run. 
:
Using mile-min we have:
:
Let t = time (minutes) running a 6 min-mile
then
(45-t) = time running a 7 min-mile
:
A distance equation in miles
{{{t/6}}} = {{{(45-t)/7}}}
Cross multiply
7t = 6(45-t)
7t = 270 - 6t
7t + 6t = 270
t = {{{270/13}}}
t = 20.77 min at a 6 min-mile
and
45 - 20.77 = 24.23 min at a 7 min-mile
:
Find the distances, (should be equal)
{{{24.23/7}}} = 3.46 mi
{{{20.77/6}}} = 3.46 mi
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total distance  6.92 mi</PRE>