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Sagot :
To solve this problem the first thing we have to do is identify our variables
The time taken by Janice will be represented by a j, and the time taken by Donald by a d.
• Donald builds the picnic table in hours: , 1/d, of the picnic table per hour
,• Janice builds the picnic table ,j=d-2, in hours: ,1/(d-2), of the picnic table per hour
Now we will get our equation to solve
Janice and Donald worked together for 2 hours to build a picnic table, after which Donald continued working for 1 hour without Janice to finish the job.
[tex]\begin{gathered} 2(\frac{1}{d}+\frac{1}{d-2})+1(\frac{1}{d})=1Table \\ \frac{2}{d}+\frac{2}{d-2}+\frac{1}{d}=1Table \\ \frac{3}{d}+\frac{2}{d-2}=1\text{Table} \\ \frac{2d+3(d-2)}{d(d-2)}=1\text{table} \\ 2d+3d-6=d^2-2d \\ d^2-2d-5d+6=0 \\ d^2-7d+6 \end{gathered}[/tex]We factor our equation to find Donald's time
[tex]\begin{gathered} (d-6)(d-1)=0 \\ d_1=6 \\ d_2=1 \end{gathered}[/tex]They gave us 2 values but we discarded the value of d=1 because the joint calculations would give negative calculations then
[tex]\begin{gathered} j=d-2 \\ j=6-2 \\ j=4 \end{gathered}[/tex]Donald takes 6 hours to set up a table and Janice takes 4 hours.
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