Question 953335
____________________speed__________time___________distance
SLOW________________r______________t+2____________170
FAST________________r+16___________t______________150


Implied variables;
RT=D uniform travel rates



Two equations in two unknown variables.  


{{{t=150/(r+16)}}}
;
{{{r((150/(r+16))+2)=170}}}
{{{150r/(r+16)+2r=170}}}
{{{150r+2r(r+16)=170(r+16)}}}
{{{150r+2r^2+32=170r+170*16}}}
{{{2r^2+32=20r+170*16}}}
{{{r^2+16=10r+170*8}}}
{{{r^2-10r+16-170*8=0}}}
{{{highlight_green(r^2-10r-1344=0)}}}



PREPARE FOR GENERAL SOLUTION FOR QUADRATIC EQUATION
Discriminant:  {{{100+4*1344=5476=(74)^2}}}
;
{{{r=(10+- 74)/2}}}, obviously the PLUS form is needed.
{{{r=(10+74)/2}}}
{{{highlight(r=42)}}}