Question 150888
Let Steve's speed = {{{r}}}
{{{d = r* t}}}
{{{600 = r*t}}}
{{{t = 600 / r}}}
{{{600 = (r + 20)*(t - 1)}}}
{{{600 = (r + 20)*((600/r) - 1)}}}
{{{600 = 600 + 12000/r - r - 20}}}
Subtract {{{600}}} from both sides
{{{0 = 12000/r - r - 20}}}
multiply both sides by {{{r}}}
{{{-r^2 - 20r + 12000 = 0}}}
Use quadratic formula to solve
{{{r = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{r = (-(-20) +- sqrt( (-20)^2-4*(-1)*12000 ))/(2*(-1)) }}} 
{{{r = (20 +- sqrt(48400 ))/-2) }}}
{{{r = (20 +- 220)/-2) }}}
{{{r = -10 + 110}}}
{{{r = -10 - 110}}}
{{{r = 100}}}
{{{r = -120}}} reject this answer- can't be negative
His speed is 100 mi/hr
check answer:
{{{600 = (r + 20)*((600/r) - 1)}}}
{{{600 = (100 + 20)*((600/100) - 1)}}}
{{{600 = 120*(6 - 1)}}}
{{{600 = 120*5}}}
{{{600 = 600}}}
OK