Question

Harvey the wonder Hamster can run 3 1/6 km in 1/4 hour. Harvey runs at a constant rate find his average speed in kilometers per hour

Answer 1

let's firstly convert the mixed fractio to improper fraction.

`\stackrel{mixed}{3(1)/(6)}\implies \cfrac{3\cdot 6+1}{6}\implies \stackrel{improper}{\cfrac{19}{6}} \\\\[-0.35em] ~\dotfill`

`\begin{array}{ccll} Km s&Hour\\ \cline{1-2} (19)/(6)&(1)/(4)\\[1em] x&1 \end{array}\implies \cfrac{~~ (19)/(6)~~}{x}~~ = ~~\cfrac{~~ (1)/(4)~~}{1}\implies \cfrac{~~ (19)/(6)~~}{(x)/(1)}=\cfrac{1}{4}\implies \cfrac{19}{6}\cdot \cfrac{1}{x}=\cfrac{1}{4} \\\\\\ \cfrac{19}{6x}=\cfrac{1}{4}\implies 76=6x\implies \cfrac{76}{6}=x\implies \cfrac{38}{3}=x\implies 12(2)/(3)=x`