Question

Harmony can paint 1/3 of a wall in

1/4 of an hour. At this rate, how long
would it take her to paint an entire wall?

Answer 1

keeping in mind that a whole is always 1 fractions wise, namely 5/5 or 1,000/1000 all equal one.

in this case we have Harmony painting 1/3 of a wall, the whole wall will be 3/3, and we also know that she can do 1/3 of the wall in 1/4 of an hour, how long will it be for the 3/3 of the wall?

`\begin{array}{ccll} wall&hour\\ \cline{1-2} (1)/(3)&(1)/(4)\\[1em] \underset{whole}{(3)/(3)}&x \end{array}\implies \cfrac{~~ (1 )/(3 ) ~~}{(3)/(3)}~~ = ~~\cfrac{~~ ( 1)/(4 ) ~~}{x}\implies \cfrac{~~ (1 )/(3 ) ~~}{(3)/(3)}~~ = ~~\cfrac{~~ ( 1)/(4 ) ~~}{(x)/(1)}\implies \cfrac{~~ ( 1)/(3 ) ~~}{1}=\cfrac{1}{4}\cdot \cfrac{1}{x} \\\\\\ \cfrac{1}{3}=\cfrac{1}{4x}\implies 4x=3\implies x=\cfrac{3}{4} ~~ \textit{of an hour}`