SOLUTION: 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.

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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.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let Steve's speed = r
d+=+r%2A+t
600+=+r%2At
t+=+600+%2F+r
600+=+%28r+%2B+20%29%2A%28t+-+1%29
600+=+%28r+%2B+20%29%2A%28%28600%2Fr%29+-+1%29
600+=+600+%2B+12000%2Fr+-+r+-+20
Subtract 600 from both sides
0+=+12000%2Fr+-+r+-+20
multiply both sides by r
-r%5E2+-+20r+%2B+12000+=+0
Use quadratic formula to solve
r+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

r+=+%2820+%2B-+sqrt%2848400+%29%29%2F-2%29+
r+=+%2820+%2B-+220%29%2F-2%29+
r+=+-10+%2B+110
r+=+-10+-+110
r+=+100
r+=+-120 reject this answer- can't be negative
His speed is 100 mi/hr
check answer:
600+=+%28r+%2B+20%29%2A%28%28600%2Fr%29+-+1%29
600+=+%28100+%2B+20%29%2A%28%28600%2F100%29+-+1%29
600+=+120%2A%286+-+1%29
600+=+120%2A5
600+=+600
OK