SOLUTION: Jon walked 5 miles to school then ran the same distance home. His speed on the trip home was 5 miles faster than the speed he had walked. If the trip home took 45 minutes less time

Algebra ->  Problems-with-consecutive-odd-even-integers -> SOLUTION: Jon walked 5 miles to school then ran the same distance home. His speed on the trip home was 5 miles faster than the speed he had walked. If the trip home took 45 minutes less time      Log On


   

Question 182633: Jon walked 5 miles to school then ran the same distance home. His speed on the trip home was 5 miles faster than the speed he had walked. If the trip home took 45 minutes less time, what was his walking speed?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Walking to school:
(1) d%5Bw%5D+=+r%5Bw%5D%2At%5Bw%5D
Running home:
(2) d%5Br%5D+=+r%5Br%5D%2At%5Br%5D
given:
(3) d%5Bw%5D+=+5 mi
(4) d%5Br%5D+=+5 mi
(5) t%5Br%5D+=+t%5Bw%5D+-+3%2F4 hr
(6) r%5Br%5D+=+r%5Bw%5D+%2B+5 mi/hr
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Now I can rewrite (1) and (2)
(1) 5+=+r%5Bw%5D%2At%5Bw%5D
(2) 5+=+%28r%5Bw%5D+%2B+5%29%2A%28t%5Bw%5D+-+3%2F4%29
(2) 5+=+r%5Bw%5D%2At%5Bw%5D+%2B+5t%5Bw%5D+-+%283%2F4%29%2Ar%5Bw%5D+-+15%2F4
(2) 5+=+5+%2B+5t%5Bw%5D+-+%283%2F4%29%2Ar%5Bw%5D+-+15%2F4
(2) 0+=+20t%5Bw%5D+-+3r%5Bw%5D+-+15
(2) 0+=+20t%5Bw%5D+-+3%2A%285%2Ft%5Bw%5D%29+-+15
(2) 20%2A%28t%5Bw%5D%29%5E2+-+15t%5Bw%5D+-+15+=+0
(2) 4%2A%28t%5Bw%5D%29%5E2+-+3t%5Bw%5D+-+3+=+0
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For now I'll say t%5Bw%5D+=+x and use the
quadratic formula
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a+=+4
b+=+-3
c+=+-3
x+=+%28-%28-3%29+%2B-+sqrt%28+%28-3%29%5E2-4%2A4%2A%28-3%29+%29%29%2F%282%2A4%29+
x+=+%28+3+%2B-+sqrt%28+9+%2B+48+%29%29%2F8+
x+=+%28+3+%2B-+sqrt%28+57+%29%29%2F8+
x+=+%28+3+%2B-+7.55%29%2F8+
x+=+10.55%2F8
x+=+1.32 hr
(1) 5+=+r%5Bw%5D%2At%5Bw%5D
(1) 5+=+1.32%2Ar%5Bw%5D
r%5Bw%5D+=+5%2F1.32
r%5Bw%5D+=+3.79 mi/hr
His walking speed was 3.79 mi/hr
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check answer
(6) r%5Br%5D+=+r%5Bw%5D+%2B+5 mi/hr
r%5Br%5D+=+3.79+%2B+5
r%5Br%5D+=+8.79 mi/hr
(1) d%5Bw%5D+=+r%5Bw%5D%2At%5Bw%5D
5+=+3.79%2At%5Bw%5D
t%5Bw%5D+=+1.32 hr
(5) t%5Br%5D+=+t%5Bw%5D+-+3%2F4 hr
t%5Br%5D+=+1.32+-+.75
t%5Br%5D+=+.57 hr
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(1) d%5Bw%5D+=+r%5Bw%5D%2At%5Bw%5D
5+=+3.79%2A1.32
5+=+5
(2) d%5Br%5D+=+r%5Br%5D%2At%5Br%5D
5+=+8.79%2A.57
5+=+5.01 close enough