Question

Yumi and Juan pick up litter along the highway at the same rate. Yumi picks up litter for 3 miles and takes two hours longer than Juan, who picks up litter for 2 miles. If it took Juan x hours, how long did it take Yumi?



1 hour 20 minutes

3 hours 20 minutes

4 hours

6 hours

Answer 1

\(\huge\color{red}{\star}\color{gold}{^\star}\color{limegreen}{_\star}\color{cornflowerblue}{\star}\color{blueviolet}{^\star}\color{violet}{\star}\color{magenta}{_\star}\color{red}{\star}\color{gold}{^\star}\color{limegreen}{_\star}\color{cornflowerblue}{\star}\color{blueviolet}{^\star}\color{violet}{\star}\color{magenta}{_\star}\color{red}{\star}\)
\(~~~~~~~~\Large\cal\color{black}{Welcome~to~OpenStudy!}\cal\hspace{-153.9pt}\color{red}{W}\color{gold}{e}\color{limegreen}{l}\color{cornflowerblue}{c}\color{blueviolet}{o}\color{violet}{m}\color{magenta}{e~}\color{red}{t}\color{gold}{o~}\color{limegreen}{O}\color{cornflowerblue}{p}\color{blueviolet}{e}\color{violet}{n}\color{magenta}{S}\color{red}{t}\color{gold}{u}\color{limegreen}{d}\color{cornflowerblue}{y}\color{blueviolet}{!}\)
\(\huge\color{red}{\star}\color{gold}{^\star}\color{limegreen}{_\star}\color{cornflowerblue}{\star}\color{blueviolet}{^\star}\color{violet}{\star}\color{magenta}{_\star}\color{red}{\star}\color{gold}{^\star}\color{limegreen}{_\star}\color{cornflowerblue}{\star}\color{blueviolet}{^\star}\color{violet}{\star}\color{magenta}{_\star}\color{red}{\star}\)

\(~~~~~~~~~~~~~~~~~~~~~~~~~\color{red}{P}\color{gold}{l}\color{limegreen}{e}\color{cornflowerblue}{a}\color{blueviolet}{s}\color{violet}{e~}\color{magenta}{R}\color{red}{e}\color{gold}{a}\color{limegreen}{d~}\color{cornflowerblue}{the}\)
\(~~~~~~~\href{https:///openstudy.com/terms-and-conditions}{\large\bf{\color{red}{\bigstar~T}}\color{orange}{e}\color{gold}{r}\color{lime}{m}\color{cyan}{s}\color{blue}{~a}\color{blueviolet}{n}\color{purple}{d}\color{orchid}{~C}\color{magenta}{o}\color{pink}{n}\color{red}{d}\color{orange}{i}\color{gold}{t}\color{lime}{i}\color{cyan}{o}\color{blue}{n}\color{blueviolet}{s}\color{red}{~\bigstar}}\)
\(~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\color{red}{a}\color{gold}{n}\color{limegreen}{d~}\color{cornflowerblue}{t}\color{blueviolet}{h}\color{violet}{e}\)
\(~~~~~~~~~~~~~~\href{https:///openstudy.com/code-of-conduct}{\large\bf{\color{red}{\bigstar~C}}\color{orange}{o}\color{gold}{d}\color{lime}{e~}\color{cyan}{o}\color{blue}{f~}\color{blueviolet}{C}\color{purple}{o}\color{orchid}{n}\color{magenta}{d}\color{pink}{u}\color{red}{c}\color{orange}{t}\color{red}{~\bigstar}}\)
\(\Large\color{green}{☙}\hspace{-2pt}\color{green}{|}\hspace{-2pt}\color{green}{❧}\hspace{-13pt}\huge\color{red}{^❀~}\Large\color{green}{☙}\hspace{-2pt}\color{green}{|}\hspace{-2pt}\color{green}{❧}\hspace{-13pt}\huge\color{gold}{^❀~}\Large\color{green}{☙}\hspace{-2pt}\color{green}{|}\hspace{-2pt}\color{green}{❧}\hspace{-13pt}\huge\color{limegreen}{^❀~}\Large\color{green}{☙}\hspace{-2pt}\color{green}{|}\hspace{-2pt}\color{green}{❧}\hspace{-13pt}\huge\color{cornflowerblue}{^❀~}\Large\color{green}{☙}\hspace{-2pt}\color{green}{|}\hspace{-2pt}\color{green}{❧}\hspace{-13pt}\huge\color{blueviolet}{^❀~}\Large\color{green}{☙}\hspace{-2pt}\color{green}{|}\hspace{-2pt}\color{green}{❧}\hspace{-13pt}\huge\color{violet}{^❀~}\Large\color{green}{☙}\hspace{-2pt}\color{green}{|}\hspace{-2pt}\color{green}{❧}\hspace{-13pt}\huge\color{magenta}{^❀~}\Large\color{green}{☙}\hspace{-2pt}\color{green}{|}\hspace{-2pt}\color{green}{❧}\hspace{-13pt}\huge\color{red}{^❀}\)

Answer 2

rate = distance/time
Juan's rate = 2/x
Yumi's rate = 3/(x+2)
The rates are equal so,
\[\frac{ 2 }{ x }=\frac{ 3 }{ x+2 }\]