Question 169541
distance = rate multiplied by time.  let r and t be rate and time of 1st car
and r+15 and t-1 be rate and time of 2nd car.
:
180=rt----------->t=180/r....eq 1
180=(r+15)(t-1)...eq 2
:
take t's value from eq 1 and substitute it into eq 2
:
{{{180=(r+15)((180/r)-1)}}}
:
{{{180=(r+15)((180-r)/r)}}}....multiply by r
{{{180r=(r+15)(180-r)}}}....distribute right side
:
{{{180r=180r-r^2+2700-15r}}}
:
{{{r^2+15r-2700=0}}} use quadratic formula
{{{highlight(r=45)}}} {{{highlight(r=-60)}}}   throw out negative value
:
{{{highlight(r=45)}}} rate of 1st car
{{{highlight(r+15=60)}}} rate of 2nd car:

*[invoke quadratic "r", 1, 15, -2700]