Question 352564
given:
{{{d = 150}}} mi
{{{d = r*t}}}
{{{150 = r*t}}}
{{{150 = (r + 10)*(t - 1/2)}}}
{{{150 = (r + 10)*(150/r - 1/2)}}}
{{{150 = 150 + 1500/r - r/2 - 5}}}
{{{1500/r - r/2 - 5 = 0}}}
{{{1500 - r^2/2 - 5r = 0}}}
{{{r^2 + 10r - 3000 = 0}}}
Use quadratic formula:
 {{{r = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{a = 1}}}
{{{b = 10}}}
{{{c = -3000}}}
 {{{r = (-10 +- sqrt( 10^2-4*1*(-3000) ))/(2*1) }}}
 {{{r = (-10 +- sqrt( 100 + 12000) ))/2 }}}
{{{r = (-10 +- sqrt(12100))/2}}}
{{{r = (-10 + 110)/2}}}
{{{r = 50}}}
The negative square root cannot be a valid speed, so
The speed of the bus is 50 mi/hr
check answer:
{{{150 = (r + 10)*(t - 1/2)}}}
{{{150 = (50 + 10)*(t - 1/2)}}}
{{{150 = 60*(t - 1/2)}}}
{{{150 = 60t - 30}}}
{{{60t = 180}}}
{{{t = 3}}} hrs
and, since
{{{150 = r*t}}}
{{{150 = 50*3}}}
{{{150 = 150}}}
OK