Question 976403


Let &nbsp;<B>x</B>&nbsp; be the speed of faster train &nbsp;(mi/h), &nbsp;and &nbsp;<B>y</B>&nbsp; be the speed of the other train (mi/h). &nbsp;Then you have the system of two linear equations in two unknowns


{{{x + y}}} = {{{440/4}}} = {{{110}}},

{{{x - y}}} = {{{12}}}.


To solve the system, &nbsp;first add both equations. &nbsp;You will get


{{{2x}}} = {{{110+12}}} = {{{122}}}. 


Hence, &nbsp;{{{x}}} = {{{122/2}}} = {{{61}}} {{{mi/h}}}. 


Now, &nbsp;substitute the found value of &nbsp;<B>x</B>&nbsp; into the first equation. &nbsp;You will get 


{{{61 + y}}} = {{{110}}}. 


Hence, &nbsp;{{{y}}} = {{{110 - 61}}} = {{{49}}} {{{mi/h}}}.


<B>Answer</B>. &nbsp;The speed of the faster train is &nbsp;61 {{{mi/h}}}. &nbsp;The speed of the other train is &nbsp;49 {{{mi/h}}}.