SOLUTION: if you can jog @ 8 miles per hour and run @ 12 mph, how much have you run and jogged if you went 6 miles in 40 minutes. Please show how to set up the equation. Thank you.

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Question 834895: if you can jog @ 8 miles per hour and run @ 12 mph, how much have you run and jogged if you went 6 miles in 40 minutes. Please show how to set up the equation. Thank you.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Let u = distance done jogging
Let v = distance done running

Know that 40 minutes is equal to 2%2F3 hour.

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Accounting for the given distance of 6 miles: u%2Bv=6
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Accounting for the given time, %282%2F3%29 hour: %281%2F8%29u%2B%281%2F2%29v=2%2F3.
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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%281%2F8%29u%2B%281%2F2%29v=2%2F3
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u%2Bv=6
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You should first simplify the time equation, multiplying both sides by 24 to start.