Question 834895
Let u = distance done jogging
Let v = distance done running


Know that 40 minutes is equal to {{{2/3}}} hour.


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Accounting for the given distance of 6 miles: {{{u+v=6}}}
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Accounting for the given time, {{{(2/3)}}} hour:  {{{(1/8)u+(1/2)v=2/3}}}.
In case this equation seems strange, rewrite each term carefully, showing the units of every number, and you should understand, the expression on the left is in units of HOURS.  
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Interesting how this is a mixture problem, as you have classified, and that the concentration is HOURS per MILE.  A better classification might be "Travel".  


That is the setup.  Solve the system:
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{{{(1/8)u+(1/2)v=2/3}}}
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{{{u+v=6}}}
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You should first simplify the time equation, multiplying both sides by 24 to start.