SOLUTION: A truck and a van left from Paris in opposite directions. The truck traveled for 8 hours at 69 mph. The vehicles were 768 miles apart. Find the van's average speed.

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Question 932526: A truck and a van left from Paris in opposite directions. The truck traveled for 8 hours at 69 mph. The vehicles were 768 miles apart. Find the van's average speed.
Answer by ptfile(81) About Me  (Show Source):
You can put this solution on YOUR website!
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+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

t+=+%28-368+%2B-+sqrt%28+135424+-4%2A%2823%29%2A%28-576%29+%29%29%2F%2846%29+
t+=+%28-368+%2B-+sqrt%28+135424%2B52992+%29%29%2F%2846%29+
t+=+%28-368+%2B-+sqrt%28+188416+%29%29%2F%2846%29+
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.