Question 323778
Equation for David:
{{{d = r*t}}}
{{{80 = r*t}}}
Equation for Keith:
{{{100 = (r + 10)*(t - 1/6)}}}
{{{100 = rt + 10t - (1/6)*r - 10/6}}}
By substitution:
{{{100 = 80 + 10t - (1/6)*(80/t) - 10/6}}}
{{{20 = 10t - (40/(3t) - 5/3)}}}
Multiply both sides by {{{3t}}}
{{{60t = 30t^2 - 40 - 5t}}}
{{{30t^2 - 65t - 40 = 0}}}
{{{6t^2 - 13t - 8 = 0}}}
Use the quadratic formula
{{{t = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{a = 6}}}
{{{b = -13}}}
{{{c = -8}}}
{{{t = (-(-13) +- sqrt( (-13)^2-4*6*(-8) ))/(2*6) }}}
{{{t = ( 13 +- sqrt(  169 + 192 ))/12 }}}
{{{t = ( 13 +- sqrt(  361 ))/12 }}}
{{{t = ( 13 +- 19)/12 }}}
{{{t = 32/12}}}
{{{t = 8/3}}}
For David:
{{{80 = r*t}}}
{{{r = 80/(8/3)}}}
{{{r = 240/8}}}
{{{r = 30}}}
David's speed is 30 mi/hr
check:
For Keith
{{{100 = (r + 10)*(t - 1/6)}}}
{{{100 = (30 + 10)*(8/3 - 1/6)}}}
{{{100 = 40*(16/6 - 1/6)}}}
{{{100 = 40*(15/6)}}}
{{{600 = 40*15}}}
{{{600 = 600}}}
OK