John walked 9 5/8 mile at an average speed of 1 3/4 mile per hour how long did it take John to walk this distance​

Question

John walked 9 5/8 mile at an average speed of 1 3/4 mile per hour how long did it take John to walk this distance​

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Vivian 1 week 2021-09-13T15:30:04+00:00 1 Answer 0

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    2021-09-13T15:31:32+00:00

    so, we know his average speed is 1¾ of a mile in 1 hour, so how long is it to cover 9⅝ miles then?

    \bf \begin{array}{ccll} miles&hour\\ \cline{1-2} 1\frac{3}{4}&1\\\\ 9\frac{5}{8}&x \end{array}\implies \cfrac{~~1\frac{3}{4}~~}{9\frac{5}{8}}=\cfrac{1}{x}\implies \cfrac{~~\frac{1\cdot 4+3}{4}~~}{\frac{9\cdot 8+5}{8}}=\cfrac{1}{x}\implies \cfrac{~~\frac{7}{4}~~}{\frac{77}{8}}=\cfrac{1}{x}

    \bf \cfrac{~~\begin{matrix} 7 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{~~\begin{matrix} 4 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\cdot \cfrac{\stackrel{2}{~~\begin{matrix} 8 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}{\underset{11}{~~\begin{matrix} 77 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}} =\cfrac{1}{x}\implies \cfrac{2}{11}=\cfrac{1}{x}\implies 2x=11\implies x=\cfrac{11}{2}\implies x=5\frac{1}{2}

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