Question 80653
This is the way I do it
d = distance
s = speed
t = time
{{{600 / s = t}}}
{{{600 / (s+20) = t - 1}}}
substitute
{{{600 / (s+20) = 600/s - 1}}}
{{{600/(s+20) - 600/s = -1}}}
{{{600(1/(s+20) - 1/s) = -1}}}
{{{1/(s+20) - 1/s = -600}}}
{{{1/s - 1/(s+20) = 600}}}
the common denominator is {{{s(s+20)}}}
{{{(s + 20 -s) / s(s+20) = 600}}}
{{{s(s+20) = 12000}}}
{{{s^2 + 20s - 12000 = 0}}}
{{{s = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{s = (-20 +- sqrt( 20^2-4*1*(-12000) ))/(2*1)}}}
{{{s = (-20 +- sqrt(400 + 48000)) / 2}}}
{{{s = (-20 +- 220) / 2}}}
{{{s = 100}}} (reject the negative answer)
check the answer
{{{600 / s = t}}}
{{{600 / (s+20) = t - 1}}}
{{{600/100 = 6}}}
{{{600 / 120 = 6 - 1}}}
{{{5 = 5}}}
OK