Answer :
Kate worked 10 hours more than Sarah. Dave worked 20 hours fewer than Sarah.
A total of 155 hours worked.
x --> Sarah
y --> Dave
z --> Kate
[tex]\begin{cases}x+y+z=155\\z=x+10\\y=x-20\end{cases}[/tex]
[tex]\begin{cases}x+x-20+x+10=155\\z=x+10\\y=x-20\end{cases}[/tex]
[tex]\begin{cases}3x=165|:3\\z=x+10\\y=x-20\end{cases}[/tex]
[tex]\begin{cases}x=55\\z=55+10\\y=55-20\end{cases}[/tex]
[tex]\begin{cases}x=55\\z=65\\y=35\end{cases}[/tex]
Now we see that Kate worked 65 hours, Dave worked 35 hours, and Sarah worked 55 hours.
A total of 155 hours worked.
x --> Sarah
y --> Dave
z --> Kate
[tex]\begin{cases}x+y+z=155\\z=x+10\\y=x-20\end{cases}[/tex]
[tex]\begin{cases}x+x-20+x+10=155\\z=x+10\\y=x-20\end{cases}[/tex]
[tex]\begin{cases}3x=165|:3\\z=x+10\\y=x-20\end{cases}[/tex]
[tex]\begin{cases}x=55\\z=55+10\\y=55-20\end{cases}[/tex]
[tex]\begin{cases}x=55\\z=65\\y=35\end{cases}[/tex]
Now we see that Kate worked 65 hours, Dave worked 35 hours, and Sarah worked 55 hours.
S+D+K=155
K=S+10
D=S-20
--------------------------------
S+(S-20)+(S+10)=155
S+S-20+S+10=155
3S-10=155
3S=165
S=165/3=55
---------------------------------
If S=55,
K=55+10=65
D=55-20=35
---------------------------------
Therefore, Sarah had worked for 55 hours, Kate had worked for 65 hours and Dave had worked for 35 hours.
K=S+10
D=S-20
--------------------------------
S+(S-20)+(S+10)=155
S+S-20+S+10=155
3S-10=155
3S=165
S=165/3=55
---------------------------------
If S=55,
K=55+10=65
D=55-20=35
---------------------------------
Therefore, Sarah had worked for 55 hours, Kate had worked for 65 hours and Dave had worked for 35 hours.