SOLUTION: you drive 1500 miles to California. On the way home, you averaged 10 miles per hour less, and the drive took you 5 extra hours. What was your average speed on the way to California

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Question 210036: you drive 1500 miles to California. On the way home, you averaged 10 miles per hour less, and the drive took you 5 extra hours. What was your average speed on the way to California?
Found 2 solutions by nyc_function, josmiceli:
Answer by nyc_function(2741) About Me  (Show Source):
You can put this solution on YOUR website!
Your equation:
(x-10)(5x) + 10(x + 5) = 1500
Can you finish now?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Write 2 sets of equations, 1 going and 1 coming back
To California:
d%5Bc%5D+=+r%5Bc%5D%2At%5Bc%5D
And back
d%5Bb%5D+=+r%5Bb%5D%2At%5Bb%5D
given:
d%5Bc%5D+=+1500 mi
d%5Bb%5D+=+1500 mi
r%5Bb%5D+=+r%5Bc%5D+-+10 mi/hr
t%5Bb%5D+=+t%5Bc%5D+%2B+5 hr
---------------------------
Now rewrite equations
d%5Bc%5D+=+r%5Bc%5D%2At%5Bc%5D
1500+=+r%5Bc%5D%2At%5Bc%5D
and
d%5Bb%5D+=+r%5Bb%5D%2At%5Bb%5D
1500+=+%28r%5Bc%5D+-+10%29%28t%5Bc%5D+%2B+5%29
1500+=+r%5Bc%5D%2At%5Bc%5D+-+10%2At%5Bc%5D+%2B+5%2Ar%5Bc%5D+-+50
Substituting
1500+=+1500+-+10%2At%5Bc%5D+%2B+5%2Ar%5Bc%5D+-+50
5r%5Bc%5D+-+10t%5Bc%5D+=+50
And from above,
1500+=+r%5Bc%5D%2At%5Bc%5D
r%5Bc%5D+=+1500%2Ft%5Bc%5D
Substituting
5%2A%281500%2Ft%5Bc%5D%29+-+10t%5Bc%5D+=+50
7500+-+10%2A%28t%5Bc%5D%29%5E2+=+50t%5Bc%5D
Rewriting:
10%2A%28t%5Bc%5D%29%5E2+%2B+50t%5Bc%5D+-+7500+=+0
%28t%5Bc%5D%29%5E2+%2B+5t%5Bc%5D+-+750+=+0
Use the quadratic formula
t%5Bc%5D+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a+=+1
b+=+5
c+=+-750
t%5Bc%5D+=+%28-5+%2B-+sqrt%28+5%5E2+-+4%2A1%2A%28-750%29+%29%29%2F%282%2A1%29+
t%5Bc%5D+=+%28-5+%2B-+sqrt%28+25+%2B+3000+%29%29%2F2+
t%5Bc%5D+=+%28-5+%2B-+55%29%2F2+
t%5Bc%5D+=+25
and
t%5Bc%5D+=+-30 (reject the negative answer)
From above:
1500+=+r%5Bc%5D%2At%5Bc%5D
1500+=+r%5Bc%5D%2A25
r%5Bc%5D+=+60
The average speed driving to California was 60 mi/hr
check answer:
1500+=+%28r%5Bc%5D+-+10%29%28t%5Bc%5D+%2B+5%29
1500+=+%2860+-+10%29%2825+%2B+5%29
1500+=+50%2A30
1500+=+1500
OK