Question

It takes zach 15 minutes to walk 7 1/2 blocks to the swimming pool. At theis rate, how many blocks can he walk in one minute? Circle the letter of the correct answer. A. 1/5 blocks. B. 1/2 blocks. C. 2 blocks. D. 5 blocks Zach chose C as the correct answer. What was his error?

Answer 1

`\bf \begin{array}{ccll} minutes&blocks\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 15&7(1)/(2)\\\\ 1&b \end{array}\implies \cfrac{15}{1}=\cfrac{7(1)/(2)}{b}\implies \cfrac{15}{1}=\cfrac{(7\cdot 2+1)/(2)}{b}\implies \cfrac{15}{1}=\cfrac{(15)/(2)}{b}`


`\bf \cfrac{15}{1}=\cfrac{(15)/(2)}{(b)/(1)}\implies \cfrac{15}{1}=\cfrac{15}{2}\cdot \cfrac{1}{b}\implies \cfrac{15}{1}=\cfrac{15}{2b}\implies 30b=15 \\\\\\ b=\cfrac{15}{30}\implies b=\cfrac{1}{2}`