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How do I write a sequence with the following information?

A runner starts a race fast, but slows down along the way.  Her starting pace was 6 minutes per mile.  After every 2 miles, she slows down by 1 minute per mile.  The sequence should show how many minutes it will take to run 12 miles.
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2 Answers

OK, let's see if we can solve this, PJ:
 
First two miles take 12 minutes total.  2 miles * 6 min. per mile = 12 minutes (miles 1 and 2)
 
After the first two miles she slows down to 7 min. per mile, so the second 2 miles takes
 
2 miles * 7 min. per mile = 14 minutes. (miles 2 and 4)
 
When the second two miles is finished she slows down to 8 min. per mile.
 
2 miles * 8 min. per mile = 16 min. (miles 5 and 6)
 
Similarly, by the times she has completed 6 miles, she slows down to 9 min. per mile
 
2 miles * 9 min. per mile = 18 minutes. (miles 7 and 8)
 
And miles 9 and 10 she has slowed to 10 min. per mile
 
2 miles * 10 min. per mile = 20 (miles 9 and 10)
 
And finally, miles 11 and 12 are accomplished at 11 min. per mile
 
2 miles * 11 min. per mile = 22 minutes
 
Trying to write this as a sequence, we would have something like:
 
Total time = (2 miles)(6 min/mile) + (2 miles)(7 min/mile) + (2 miles)(8 min/mile) + (2 miles)(9 min/mile) + (2 miles)(10 min/mile) + (2 miles)(11 min/mile)
 
We could write this more compactly as
 
                                s = 11
Total time = (2 miles)∑ s
                                s = 6
 
where I have allowed s to signify her speed (expressed in min/mile).
 
Total time = (2 miles)*(6 + 7+ 8 + 9 +10 + 11)
 
               = (2 miles)(51 min/mile) = 102 minutes
 

Comments

Hi Pj;
WILLIAM IS CORRECT.  MY APOLOGIES...
(6 minutes/mile)(2 miles)=12 minutes
(7 minutes/mile)(2 miles)=14 minutes
(8 minutes/mile)(2 miles)=16 minutes
(9 minutes/mile)(2 miles)=18 minutes
(10 minutes/mile)(2 miles)=20 minutes
(11 minutes/mile)(2 miles)=22 minutes
TOTAL.............................102 minutes
Please note that the unit of miles is always in the denominators and numerators.  Therefore, these cancel leaving the unit of minutes equal to minutes.

Comments

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