Question

A car is traveling at a steady speed. It travels 1 3/4 miles in 2 1/3 minutes. How far will it travel in 27 minutes ​? In 1 hour ​?

Answer 1

now, let's convert all mixed fractions to improper fractions. Let's recall that 1 hour is 60 minutes.

`\stackrel{mixed}{1(3)/(4)}\implies \cfrac{1\cdot 4+3}{4}\implies \stackrel{improper}{\cfrac{7}{4}}~\hfill \stackrel{mixed}{2(1)/(3)} \implies \cfrac{2\cdot 3+1}{3} \implies \stackrel{improper}{\cfrac{7}{3}} \\\\[-0.35em] ~\dotfill`

`\begin{array}{ccll} miles&minutes\\ \cline{1-2} (7)/(4)&(7)/(3)\\[1em] m&27 \end{array}\implies \implies \cfrac{~~ ( 7 )/( 4 ) ~~}{m}~~ = ~~\cfrac{~~ ( 7 )/( 3 ) ~~}{27}\implies \cfrac{7}{4m}=\cfrac{7}{3}\cdot \cfrac{1}{27} \\\\\\ \cfrac{7}{4m}=\cfrac{7}{81}\implies 567=28m\implies \cfrac{567}{28}=m\implies \cfrac{81}{4}=m\implies 20(1)/(4)=m \\\\[-0.35em] ~\dotfill`

`\begin{array}{ccll} miles&minutes\\ \cline{1-2} (7)/(4)&(7)/(3)\\[1em] m&60 \end{array}\implies \implies \cfrac{~~ ( 7 )/( 4 ) ~~}{m}~~ = ~~\cfrac{~~ ( 7 )/( 3 ) ~~}{60}\implies \cfrac{7}{4}\cdot \cfrac{1}{m}=\cfrac{7}{3}\cdot \cfrac{1}{60} \\\\\\ \cfrac{7}{4m}=\cfrac{7}{180}\implies 1260=28m\implies \cfrac{1260}{28}=m\implies 45=m`

Answer 2

Explanation:

`1(3)/(4) =(7)/(4) ~milles\\2(1)/(3) =(7)/(3) ~minutes\\1~hr=60~nutes\\distance~covered~in~(7)/(3) ~minutes=(7)/(4) ~miles\\distance~covered~in~1~minutes=(7)/(4) * (3)/(7) =(3)/(4) ~miles\\distance~covered~in~27~minutes=(3)/(4) * 27=(81)/(4) =20(1)/(4) ~miles\\distance~covered~in~60~minutes=(3)/(4) *60=45~miles`