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January 24th, 2012, 03:25 AM   #1
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Text exercise

At a high-school cross-country 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?
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January 24th, 2012, 03:37 AM   #2
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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?
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January 24th, 2012, 03:40 AM   #3
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Re: Text exercise

8(2-x)+12x=21
16-8x+12x=21
x=1,25
2-1,25=0,75
1,25*12=15
0,75*8=6
15+6=21
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January 24th, 2012, 04:11 AM   #4
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Re: Text exercise

The correct answer is 15 miles.
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January 24th, 2012, 04:28 AM   #5
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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 ?
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January 24th, 2012, 04:45 AM   #6
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Re: Text exercise

Yes, that is correct.
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January 24th, 2012, 04:51 AM   #7
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Re: Text exercise

30(1.5-t) + 60t = 72
45 - 30t + 60t = 72
30t = 27
t = 0.9
1.5 - 0.9 = 0.6
60 * 0.6 = 36

this is correct ?
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January 24th, 2012, 04:55 AM   #8
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Re: Text exercise

Yes; good work.
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January 24th, 2012, 05:10 AM   #9
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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
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January 24th, 2012, 05:17 AM   #10
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Re: Text exercise

Quote:
Originally Posted by thinkfast
30(1.5-t) + 60t = 72
45 - 30t + 60t = 72
30t = 27
t = 0.9
1.5 - 0.9 = 0.6
60 * 0.6 = 36
Here, t represents the amount of time Jeff traveled at 60 mph. You correctly calculated t and then subtracted that from 1.5 to get 0.6, which is how long Jeff traveled in the construction zone.

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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