Questions on Word Problems: Travel and Distance answered by real tutors!

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Question 150888: 3. Steve traveled 600 miles at a certain speed. Had he gone 20mph faster, the trip would have taken 1 hour less. Find the speed of his vehicle.: 3. Steve traveled 600 miles at a certain speed. Had he gone 20mph faster, the trip would have taken 1 hour less. Find the speed of his vehicle.
Answer by josmiceli(1827) About Me  (Show Source):
You can put this solution on YOUR website!
Let Steve's speed = r
d = r* t
600 = r*t
t = 600 / r
600 = (r + 20)*(t - 1)
600 = (r + 20)*((600/r) - 1)
600 = 600 + 12000/r - r - 20
Subtract 600 from both sides
0 = 12000/r - r - 20
multiply both sides by r
-r^2 - 20r + 12000 = 0
Use quadratic formula to solve
r = (-b +- sqrt( b^2-4*a*c ))/(2*a)
r = (-(-20) +- sqrt( (-20)^2-4*(-1)*12000 ))/(2*(-1))
r = (20 +- sqrt(48400 ))/-2)
r = (20 +- 220)/-2)
r = -10 + 110
r = -10 - 110
r = 100
r = -120 reject this answer- can't be negative
His speed is 100 mi/hr
check answer:
600 = (r + 20)*((600/r) - 1)
600 = (100 + 20)*((600/100) - 1)
600 = 120*(6 - 1)
600 = 120*5
600 = 600
OK