Question

How long will it take an object to travel 5 1/5 when it travels 8 2/3 miles per hour

Answer 1

let's first convert the mixed fractions to improper, and then proceed.

$\bf \stackrel{mixed}{5\frac{1}{5}}\implies \cfrac{5\cdot 5+1}{5}\implies \stackrel{improper}{\cfrac{26}{5}}~\hfill \stackrel{mixed}{8\frac{2}{3}}\implies \cfrac{8\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{26}{3}}\\\\[-0.35em]\rule{34em}{0.25pt}\\\\\begin{array}{ccll}miles&hours\\\cline{1-2}\\\frac{26}{3}&1\\[0.8em]\frac{26}{5}&h\end{array}\implies \cfrac{~~\frac{26}{3}~~}{\frac{26}{5}}=\cfrac{1}{h}\implies \cfrac{26}{3}\cdot \cfrac{5}{26}=\cfrac{1}{h}\implies \cfrac{5}{3}=\cfrac{1}{h}$

$\bf h=\cfrac{3\cdot 1}{5}\implies h=\cfrac{3}{5}\impliedby \textit{36 minutes}$

Answer 2

I alkeast need 20 characters long.