SOLUTION: Debbie traveled by boat 5 miles upstream to fish in her favorite spot. Because of the 4-mph current, it took her 20 minutes longer to get their than to return. How fast will her bo

Algebra ->  Rational-functions -> SOLUTION: Debbie traveled by boat 5 miles upstream to fish in her favorite spot. Because of the 4-mph current, it took her 20 minutes longer to get their than to return. How fast will her bo      Log On


   



Question 172553: Debbie traveled by boat 5 miles upstream to fish in her favorite spot. Because of the 4-mph current, it took her 20 minutes longer to get their than to return. How fast will her boat go in still water?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let s= her speed in still water
Let c= the speed of the current
Let d= the distance she has to go
Let t%5Bu%5D= time going upstream in hrs
Let t%5Bd%5D= time going downstream in hrs
Then
s+-+c= speed of boat going upstream
s+%2B+c= speed of boat going downstream
----------------
The problem says
c+=+4 mi/hr
t%5Bu%5D+=+t%5Bd%5D+%2B+%281%2F3%29
d+=+5 mi
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d+=+%28s+-+c%29%2At%5Bu%5D going upstream
5+=+%28s+-+4%29%2A%28t%5Bd%5D+%2B+%281%2F3%29%29
5+=+t%5Bd%5D%2As+-+4t%5Bd%5D+%2B+%281%2F3%29%2As+-+%284%2F3%29
and, going downstream
5+=+%28s+%2B+4%29%2At%5Bd%5D
t%5Bd%5D+=+5+%2F+%28s+%2B+4%29
Substitute this into the upstream equation
5+=+%285%2F%28s+%2B+4%29%29%2As+-+4%2A5+%2F+%28s+%2B+4%29+%2B+%281%2F3%29%2As+-+4%2F3
Multiply both sides by 3%2A%28s+%2B+4%29
15%2A%28s+%2B+4%29+=+15s+-+60+%2B+s%2A%28s+%2B+4%29+-+4%2A%28s+%2B+4%29
15s+%2B+60+=+15s+-+60+%2B+s%5E2+%2B+4s+-+4s+-+16
s%5E2+-+120+-+16+=+0
s%5E2+-+136+=+0
s%5E2+=+136
s+=+11.662 mi/hr
The speed of the boat in still water is 11.662 mi/hr
check answer:
s+-+c+=+s+-+4
s+-+4+=+7.662
s+%2B+c+=+s+%2B+4
s+%2B+4+=+15.662
t%5Bd%5D+=+5+%2F+%28s+%2B+4%29
t%5Bd%5D+=+5+%2F+15.662
t%5Bd%5D+=+.319hrs
t%5Bu%5D+=+t%5Bd%5D+%2B+%281%2F3%29
t%5Bu%5D+=+.6525hrs
d+=+%28s+-+c%29%2At%5Bu%5D going upstream
5+=+7.662%2A.6525
5+=+4.9998 close enough
also
d+=+%28s+%2B+c%29%2At%5Bd%5D
5+=+15.662%2A.319
5+=+4.996 close enough