Question

A construction crew has just finished building a road. The crew worked for 9 days. If they built 3 5/6 kilometers of road each day, what is the total length of road they built?Write your answer as a mixed number in simplest form.

Answer 1

Step-by-step explanation

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:

`3(5)/(6)=3+(5)/(6)=(3\cdot6)/(6)+(5)/(6)=(18)/(6)+(5)/(6)=(23)/(6).`

The number of km of road built was:

`\begin{gathered} \text{\# of days }*\text{ km built per day} \\ =9\text{ days}*(23)/(6)\frac{\text{km}}{\text{day}} \\ =(9\cdot23)/(6)km. \end{gathered}`

We simplify the last result:

`(9\cdot23)/(6)=((3\cdot3)\cdot23)/((2\cdot3))=(3\cdot23)/(2)=(69)/(2)=(68+1)/(2)=(68)/(2)+(1)/(2)=34+(1)/(2)=34(1)/(2).`Answer

The total length of the road they built is 34 1/2 km.