From the statement, we know that:
• the crew worked for 9 days,
,• they built 3 5/6 km of road per day.
We write the number of km per day in simple form:
[tex]3\frac{5}{6}=3+\frac{5}{6}=\frac{3\cdot6}{6}+\frac{5}{6}=\frac{18}{6}+\frac{5}{6}=\frac{23}{6}.[/tex]The number of km of road built was:
[tex]\begin{gathered} \text{\# of days }\times\text{ km built per day} \\ =9\text{ days}\times\frac{23}{6}\frac{\text{km}}{\text{day}} \\ =\frac{9\cdot23}{6}km. \end{gathered}[/tex]We simplify the last result:
[tex]\frac{9\cdot23}{6}=\frac{(3\cdot3)\cdot23}{(2\cdot3)}=\frac{3\cdot23}{2}=\frac{69}{2}=\frac{68+1}{2}=\frac{68}{2}+\frac{1}{2}=34+\frac{1}{2}=34\frac{1}{2}.[/tex]AnswerThe total length of the road they built is 34 1/2 km.
