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In the following, t will represent the unknown time
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CHAPTER 8 Linear Applications
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Worker Sherry Denise Together Quantity 1 1 1 Rate 1=t 1/30 1/20 Time t 30 20
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The equation to solve is 1=t 1=30 1=20 The LCD is 60t 1 1 1  t 30 20    1 1 1 60t 60t t 30 20     1 1 60t 3t 60t t 30 60 2t 3t 2t 2t 60 t Alone, Denise can mow the yard in 60 minutes 2
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Worker Ben Brandon Together Quantity 1 1 1 Rate 1/3 1=t 1=2 Time 3 t 2
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The equation to solve is 1=3 1=t 1=2 The LCD is 6t 1 1 1 t  3  2  1 1 1 6t 6t 3 t 2     1 1 6t 6t 3t 3 t 2t 6 3t 2t 2t 6 t
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CHAPTER 8 Linear Applications
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Brandon can split the wood-pile by himself in 6 hours 3
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Worker Boy Girl Together Quantity 1 1 1 Rate 1/90 1/60 1=t Time 90 60 t
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The equation to solve is 1=90 1=60 1=t The LCD is 180t 1 1 1  90 60 t    1 1 1 180t 180t 90 60 t     1 1 180t 180t 180 90 60 2t 3t 180 5t 180 180 t 5 t 36 Working together, the boy and girl need 36 minutes to weed the garden 4
Worker Robert Paul Together Quantity 1 1 1 Rate 1/40 1/20 1=t Time 40 20 t
The equation to solve is 1=40 1=20 1=t The LCD is 40t
CHAPTER 8 Linear Applications
1 1 1 40 20 t     1 1 1 40t 40t 40 20 t     1 1 40t 40 40t 40 20 t 2t 40 3t 40 40 13 1 t 3 3 Together Robert and Paul can assemble the bookcase in 131 3 minutes or 13 minutes 20 seconds 5
Worker Pipe I Quantity 1 Rate 6/7 1 6=7 7=6 Pipe II Together 1 1 1=t 4/3 1 4=3 3=4 t 3/4 Time 7/6
The equation to solve is 6=7 1=t 4=3 The LCD is 21t 6 1 4 t  7  3   6 1 4 21t 21t 7 t 3     6 1 21t 28t 21t 7 t 18t 21 28t 18t 18t 21 10t 21 t 10
CHAPTER 8 Linear Applications
1 Alone, Pipe II can ll the reservoir in 210 hours or 2 hours, 6 1 1 1 minutes (10 of an hour is 10 of 60 minutes and 10 60 6)
Worker Pipe I
Quantity 1
Rate 2/13 1 2=13 13=2
Time 61 13=2 2
Pipe II
3/13 1 3=13 13=3
4 1 13=3 3
Together
The equation to solve is 2=13 3=13 1=t The LCD is 13t 2 3 1 13 13 t     2 3 1 13t 13t 13 13 t     2 3 13t 13t 13 13 13 2t 3t 13 5t 13 13 5 Together the pipes can drain the reservoir in 23 hours or 2 hours 36 5 minutes (3 of hour is 3 of 60 minutes and 3 60 36) 5 5 5 t Some work problems require part of the work being performed by one worker before the other worker joins in, or both start the job and one nishes the job In these cases, the together quantity and one of the individual quantities will not be 1 Take the time the one worker works alone divided by the time that worker requires to do the job alone, then subtract from 1 This is the proportion left over for both to work together
CHAPTER 8 Linear Applications
Examples
Jerry needs 40 minutes to mow the lawn Lou can mow the same lawn in 30 minutes If Jerry works alone for 10 minutes then Lou joins in, how long will it take for them to nish the job Because Jerry worked for 10 minutes, he did 10=40 1 of the job 4 alone So, there is 1 1 3 of the job remaining when Lou started 4 4 working Let t represent the number of minutes they worked together after Lou joins in Even though Lou does not work the entire job, his rate is still 1/30
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