car traveled 576 mi averaging a certain speed. If the car had gone 8 mph faster, the trip would have taken 1 hour less. Find the average speed.

Answer:64mi/hour

Step-by-step explanation:

V=speed * time

V=s*t ... equation (1)

v=576

for taking one hour: t-1

speed is: s+8

From equation (1)

V = (s+8) (t-1)

(s+8) (t-1) = 576

Expand the bracket

st-s+8t-8=576

Substitute the value of st which is 576

576-s+8t-8=576

Collect the like terms

-s+8t-8=0

s=8t-8

Subtitude into the value of s

576 = (8t-8) * t

576=8t^2-8t

8t^2-8t=576

8t^2-8t-576=0 (divide both by 8)

t^2-t-72=0

By factorization method

Product is (-9 and 8)

(t-9) (t+8) = 0

t=9 or t=-8

V=s*t

576=s*9

9s=576

s=576/9

s=64mi/hour