Question

A 16 1/2 kilometer stretch of road needs repairs. Workers can repair 2 1/4- kilometer of road per week. 16 1 How many weeks will it take to repair this stretch of road? weeks Report a problem Stuck? Watch a video or use a hint. Get 5 of 7 questions to level up to Familiar

Answer 1

7.33 weeks

Step-by-step explanation

you can easily solve this by using a rule of three

Step 1

if workers can repair 2 1/4 kilometers per week

`\begin{gathered} 2(1)/(4)\rightarrow1\text{ w}eek \\ 2.25\rightarrow1\text{ w}eek \\ the\text{ proportion is=}\frac{2.25\text{ km}}{1\text{ w}eek}=2.25\text{ kilometers per w}eek \\ \end{gathered}`

Step 2

Let

x represents the number of weeks will take to repair the full stretch

then

`\begin{gathered} 16(1)/(2)km\rightarrow x \\ 16.5\text{ km}\rightarrow x \\ \text{the proportion is=}\frac{16.5\text{ km}}{x} \end{gathered}`

Step 3

as the proportions are the same

`\begin{gathered} 2.25=(16.5)/(x) \\ \text{solve for x} \\ x=(16.5)/(2.25) \\ x=7.33 \end{gathered}`

Hence, the answer is 7.33 weeks