SOLUTION: A Car is driven 280 mi. if it had gone 5mph faster, it could have made the trip in 1hr less time. What is the speed?

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Question 286193: A Car is driven 280 mi. if it had gone 5mph faster, it could have made the trip in 1hr less time. What is the speed?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Write 2 equations, 1 for each case:
d+=+r%2At
case #1
280+=+rt
280+=+%28r+%2B+5%29%2A%28t+-+1%29
280+=+rt+%2B+5t+-+r+-+5
By substitution:
280+=+280+%2B+5t+-+r+-+5
0+=+5t+-+r+-+5
r+=+5t+-+5
Substituting again:
280+=+%285t+-+5%29%2At
280+=+5t%5E2+-+5t
t%5E2+-+t+-+56+=+0
%28t+%2B+7%29%28t+-+8%29+=+0
t can't be negative, so t+=+8
and
280+=+rt
280+=+r%2A8
r+=+35 mi/hr
check answer:
280+=+%28r+%2B+5%29%2A%28t+-+1%29
280+=+%2835+%2B+5%29%2A%28t+-+1%29
280+=+40t+-+40
320+=+40t
t+=+8
OK