Question 571733
Let {{{p}}} be the speed of the passenger train in mph.
The speed of the freight train, in mph, is {{{p-8}}}.
Multiplying the speed in mph times the time the train has been moving, we get the distance train has moved.
When the passenger train overtakes the freight train, it has been moving for 14.25 hours at speed {{{p}.
The distance it has moved, in miles, is
{{{14.25p}}}
Until it is overtaken, the freight train has been moving for {{{3+14.25}}} hours at speed {{{8-p}}}.
The distance it has moved, in miles, is
{{{(3+14.25)(p-8)=17.25(p-8)=17.25p-17.25*8=17.25p-138}}}.
Since both trains traveled the same distance,
{{{14.25p=17.25p-138}}} --> {{{14.25p+138=17.28p-138+138}}} --> {{{14.25p+138=17.25p}}} --> {{{14.25p+138-14.25p=17.25p-14.25p}}} --> {{{138=(17.25-14.25)p}}} --> {{{138=3p}}}  --> {{{138/3=3p/3}}} --> {{{46=p}}} or {{{highlight(p=46)}}}