Question

melania walked her dogs 2 1/5 miles cathay walked her dog 1 3/4 times as far as Melania how many more miles did Cathay walk her dog

Answer 1

Melanie walked her dog 3 17/20 more miles than Cathay

Answer 2

First off, let's keep in mind that a "whole" is a 1 unit, namely, same/same, in this case, we can say that four fourths is one whole, namely 4/4 is 1 whole.

so, we know Melania walked her dog 2 and 1/5 miles, that'd be a whole, or 4/4.

we also know that Cathay walks hers 1 and 3/4 of that, hmmmm let's convert both fractions to "improper" and take it from there.

$\bf \begin{array}{lccll} &miles&\stackrel{whole}{fraction}\\ &\text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ Melania&2\frac{1}{5}&\frac{4}{4}\\\\ Cathay&x&1\frac{3}{4} \end{array}\implies \cfrac{2\frac{1}{5}}{x}=\cfrac{\frac{4}{4}}{1\frac{3}{4}}\implies \cfrac{\frac{2\cdot 5+1}{5}}{x}=\cfrac{\frac{4}{4}}{\frac{1\cdot 4+3}{4}}$

$\bf \cfrac{\frac{11}{5}}{\frac{x}{1}}=\cfrac{\frac{4}{4}}{\frac{7}{4}}\implies \cfrac{11}{5}\cdot \cfrac{1}{x}=\cfrac{4}{4}\cdot \cfrac{4}{7}\implies \cfrac{11}{5x}=\cfrac{4}{7}\implies 77=20x \\\\\\ \cfrac{77}{20}=x\impliedby \textit{Cathay does that many miles, what's their \underline{difference}?} \\\\\\ \stackrel{Cathay}{\cfrac{77}{20}}~~-~~\stackrel{Melania}{\cfrac{11}{5}}\impliedby \stackrel{LCD}{20}\implies \cfrac{77-44}{20}\implies \cfrac{33}{20}\implies 1\frac{13}{20}$