January 24th, 2012, 03:25 AM  #1 
Member Joined: Jan 2012 Posts: 33 Thanks: 0  Text exercise
At a highschool crosscountry meet, Jared jogged 8 mph for the first part of the race, then increased his speed to 12 mph for the second part. If the race was 21 mi long and Jared finished in 2 hr, how far did he jog at the faster pace? 
January 24th, 2012, 03:37 AM  #2 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,932 Thanks: 1127 Math Focus: Elementary mathematics and beyond  Re: Text exercise
Let x be how long Jared ran at 8 mph and y be how long Jared ran at 12 mph. Distance equals speed multiplied by time: 8x + 12y = 21 Total time for the trip was 2 hours, so we have the system 8x + 12y = 21 x + y = 2. Can you work with that? 
January 24th, 2012, 03:40 AM  #3 
Newbie Joined: Oct 2011 From: Turkey Posts: 29 Thanks: 0  Re: Text exercise
8(2x)+12x=21 168x+12x=21 x=1,25 21,25=0,75 1,25*12=15 0,75*8=6 15+6=21 
January 24th, 2012, 04:11 AM  #4 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,932 Thanks: 1127 Math Focus: Elementary mathematics and beyond  Re: Text exercise
The correct answer is 15 miles.

January 24th, 2012, 04:28 AM  #5 
Member Joined: Jan 2012 Posts: 33 Thanks: 0  Re: Text exercise
Jeff had a job interview in a nearby city 72 mi away. On the first leg of the trip he drove an average of 30 mph through a long construction zone, but was able to drive 60 mph after passing through this zone. If driving time for the trip was 1 1/2 hr, how long was he driving in the construction zone? I got answer 36min, correct ? 
January 24th, 2012, 04:45 AM  #6 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,932 Thanks: 1127 Math Focus: Elementary mathematics and beyond  Re: Text exercise
Yes, that is correct.

January 24th, 2012, 04:51 AM  #7 
Member Joined: Jan 2012 Posts: 33 Thanks: 0  Re: Text exercise
30(1.5t) + 60t = 72 45  30t + 60t = 72 30t = 27 t = 0.9 1.5  0.9 = 0.6 60 * 0.6 = 36 this is correct ? 
January 24th, 2012, 04:55 AM  #8 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,932 Thanks: 1127 Math Focus: Elementary mathematics and beyond  Re: Text exercise
Yes; good work.

January 24th, 2012, 05:10 AM  #9 
Member Joined: Jan 2012 Posts: 33 Thanks: 0  Re: Text exercise
But it says how long was he driving in the construction zone? So I would need to find how long he drove when his speed was 30mph ? 60t + 30t = 72 t = 0.8 * 1.5 = 1.2 30 * 1.2 = 36 too So which one ? I'm mixed up 
January 24th, 2012, 05:17 AM  #10  
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,932 Thanks: 1127 Math Focus: Elementary mathematics and beyond  Re: Text exercise Quote:
0.6 x 60 = 36 minutes, and that is the correct answer. To avoid confusion, choose the method you are most comfortable with and work with that.  

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