Road repairs

A 16 1/2 kilometer stretch of road needs repairs. Workers can repair 2 1/4 kilometers of road per week. How many weeks will it take to repair this stretch of road?

Correct answer:

w =  7 ¹⁄₃ = 22/3

Step-by-step explanation:

$$\begin{gathered} s=16\frac{1}{2}=16+\frac{1}{2}=\frac{16\cdot 2+1}{2}=\frac{32+1}{2}=\frac{33}{2}=16\frac{1}{2}=16.5\text{km} \\ r=2\frac{1}{4}=2+\frac{1}{4}=\frac{2\cdot 4+1}{4}=\frac{8+1}{4}=\frac{9}{4}=2\frac{1}{4}=2.25\text{km} \\ w=s/r=\frac{33}{2}/\frac{9}{4}=\frac{33}{2}:\frac{9}{4}=\frac{33}{2}\cdot \frac{4}{9}=\frac{33\cdot 4}{2\cdot 9}=\frac{132}{18}=\frac{22}{3}=7\frac{1}{3}=7.3333 \end{gathered}$$

Try another example