Question 932526
Let r = speed of the van 
    t = time of the van travels
 8hrs = time of the truck travels
69mph = speed of the truck
  768 = total distance
D= rt
D=(69)(8)
D= 552

Van's distance
768-552=216

r=D/t

Van's rate - Total rate = Truck's rate

      216/t - 768/(t+8) =69
                  216/t =768/(t+8)+69
                  216/t =(768+69t+552)/(t+8)
                  216/t =(1320+69t)/(t+8)
          (216t+1728)/t =1320+69t
              216t+1728 =69t^2+1320t
                   1728 =69t^2+1104t
                      0 =69t^2+1104t-1728
                      0 =23t^2+368t-576
Use quadratic formula to solve for t
{{{t = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{t = (-(368) +- sqrt( (368)^2-4*(23)*(-576) ))/(2*(23)) }}}   
{{{t = (-368 +- sqrt( 135424 -4*(23)*(-576) ))/(46) }}}
{{{t = (-368 +- sqrt( 135424+52992 ))/(46) }}}
{{{t = (-368 +- sqrt( 188416 ))/(46) }}}

t=   1.4362851939134165413072088022609 or 1
t= -17.436285193913416541307208802261 or -17 

Substitute t with 1
1+8=9
d=rt
216=(r)(9)
24=r

Substitute t with -17
-17+8=-9
d=rt
216=(r)(-9)
-24=r

The van's average speed is 24 mph.