SOLUTION: During the first part of a canoe trip, covered 75 miles at a certain speed. He then traveled 18 mile at a speed that was 5 slower. If the total time for the canoe trip was 3 hr, wh

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Question 159082: During the first part of a canoe trip, covered 75 miles at a certain speed. He then traveled 18 mile at a speed that was 5 slower. If the total time for the canoe trip was 3 hr, what was his speed on each part of the trip?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
For the two parts of the trip:
d%5B1%5D+=+r%5B1%5D%2At%5B1%5D
d%5B2%5D+=+r%5B2%5D%2At%5B2%5D
given:
d%5B1%5D+=+75mi
d%5B2%5D+=+18mi
r%5B2%5D+=+r%5B1%5D+-+5
t%5B1%5D+%2B+t%5B2%5D+=+3hr
t%5B2%5D+=+3+-+t%5B1%5Dhr
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d%5B1%5D+=+r%5B1%5D%2At%5B1%5D
75+=+r%5B1%5D%2At%5B1%5D
(1)t%5B1%5D+=+75+%2F+r%5B1%5D
and
d%5B2%5D+=+r%5B2%5D%2At%5B2%5D
18+=+%28r%5B1%5D+-+5%29%2A%283+-+t%5B1%5D%29
18+=+3r%5B1%5D+-+15+-+r%5B1%5D%2At%5B1%5D+%2B+5t%281%29
Note that r%5B1%5D%2At%5B1%5D+=+75 (given)
18+=+3r%5B1%5D+-+15+-+75+%2B+5t%5B1%5D
3r%5B1%5D+%2B+5t%5B1%5D+=+108
from (1)
3r%5B1%5D+%2B+5%2A%2875%2Fr%5B1%5D%29+=+108
multiply both sides by r%5B1%5D
3%28r%5B1%5D%29%5E2+%2B+375+=+108r%5B1%5D
subtract 108r%5B1%5D from both sides
divide both sides by 3
%28r%5B1%5D%29%5E2+-+36r%5B1%5D+%2B+125+=+0
use the quadratic formula
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
where
a+=+1
b+=+-36
c+=+125
r%5B1%5D+=+%28-%28-36%29+%2B-+sqrt%28+%28-36%29%5E2-4%2A1%2A125+%29%29%2F%282%2A1%29+
r%5B1%5D+=+%2836+%2B-+sqrt%28+1296+-+500+%29%29+%2F+2+
r%5B1%5D+=+%2836+%2B-+sqrt%28796%29%29+%2F+2+
r%5B1%5D+=+%2836+%2B+28.21%29+%2F+2+
r%5B1%5D+=+%2836+-+28.21%29+%2F+2+
r%5B1%5D+=+64.21%2F2
r%5B1%5D+=+32.1mi/hr
Using the (-) sign, the other answer is
r%5B1%5D+=+3.90mi/hr (makes no sense, too small)
---------------------
check the 1st answer:
r%5B2%5D+=+r%5B1%5D+-+5
r%5B2%5D+=+27.1mi/hr
----------------------
75+=+32.1%2At%5B1%5D
t%5B1%5D+=+2.34hr
18+=+r%5B2%5D%2At%5B2%5D
18+=+27.1%2At%5B2%5D
t%5B2%5D+=+.664hr
----------------------
The total time for the trip must be 3hr
t%5B1%5D+%2B+t%5B2%5D+=+3
2.34+%2B+.664+=+3
3.004+=+3 close enough
The speed for the 1st part was 32.1 mi/hr
The speed for the 2nd part was 27.1 mi/hr