SOLUTION: Steve traveled 150 miles at a certain speed. Had he gone 20mph faster, the trip would have taken 2 hours less. Find the speed of his vehicle.

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Question 179409: Steve traveled 150 miles at a certain speed. Had he gone 20mph faster, the trip would have taken 2 hours less. Find the speed of his vehicle.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
(1) 150+=+r%2At
(2) 150+=+%28r+%2B+20%29%2A%28t+-+2%29
Subtract (1) from (2)
0+=+%28r+%2B+20%29%28t+-+2%29+-+r%2At
r%2At+=+r%2At+%2B+20t+-+2r+-+40
2r+=+20t+-+40
And, since
150+=+r%2At
t+=+150%2Fr
2r+=+20%2A%28150%2Fr%29+-+40
2r%5E2+=+3000+-+40r
2r%5E2+%2B+40r+-+3000+=+0
r%5E2+%2B+20r+-+1500+=+0
Solve by completing the square
r%5E2+%2B+20r+%2B+%2820%2F2%29%5E2+=+1500+%2B+%2820%2F2%29%5E2
Notice the left side is a perfect square
And so is the right side
%28r+%2B+10%29%5E2+=+1600
Take the square root of both sides
r+%2B+10+=+40
r+=+30
The speed is 30 mi/hr
check:
(1) 150+=+30%2At
t+=+5 hrs
(2) 150+=+%28r+%2B+20%29%2A%28t+-+2%29
(2) 150+=+%2830+%2B+20%29%2A%28t+-+2%29
(2) 150+=+50%2A%28t+-+2%29
3+=+t+-+2
t+=+5 hrs
OK