Question 72144
total time = 120 - 12 sec
total time = 108 sec
r = rate going up
t = time to go up
{{{r*t + (r+1)*(108-t) = 480}}}
{{{r*t = 240}}}
{{{r = 240/t}}}
{{{r*t + (r+1)*(108-t) = 480}}}
{{{240 + (r+1)*(108-t) = 480}}}
{{{108r + 108 -rt - t = 240}}}
{{{108r - 240/r = 372}}}
{{{108r^2 - 372r - 240 = 0}}}
{{{r = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{r = (-(-372) +- sqrt( (-372)^2-4*108*(-240) ))/(2*108) }}}
{{{r = (372 +- sqrt(138384 + 103680 ))/216 }}}
{{{r = (372 +- sqrt(242064 ))/216 }}}
{{{r = (372 + 492) / 216}}}
{{{r = 864/216}}}
{{{r = 4}}} m/sec answer
check answer
{{{r*t = 240}}}
{{{t = 240/4}}}
{{{t = 60}}} sec
{{{r*t + (r+1)*(108-t) = 480}}}
{{{4*60 + (4+1)*(108-60) = 480}}}
{{{240 + 5*48 = 480}}}
{{{240 + 240 = 480}}}
OK