Question

Ben jogged 4 and 1/2 miles in 1 and 1/4 hours at a constant rate. How far did Ben jog in one hour? *

Answer 1

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

`\stackrel{mixed}{4(1)/(2)}\implies \cfrac{4\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{9}{2}}~\hfill \stackrel{mixed}{1(1)/(4)}\implies \cfrac{1\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{5}{4}} \\\\[-0.35em] ~\dotfill`

`\begin{array}{ccll} miles&hours\\ \cline{1-2} (9)/(2)&(5)/(4)\\[1em] x&1 \end{array}\implies \cfrac{~~ (9)/(2)~~}{x}=\cfrac{~~ (5)/(4)~~}{1}\implies \cfrac{~~ (9)/(2)~~}{(x)/(1)}=\cfrac{5}{4}\implies \cfrac{9}{2}\cdot \cfrac{1}{x}=\cfrac{5}{4} \\\\\\ \cfrac{9}{2x}=\cfrac{5}{4}\implies 36=10x\implies \cfrac{36}{10}=x\implies \cfrac{18}{5}=x\implies 3(3)/(5)=x`