SOLUTION: Please help. 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 there than to return. How fa

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Question 178714: Please help.
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 there 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 the speed of her boat in still water = s
Let the speed of the current = c
Against the current:
d%5B1%5D+=+r%5B1%5D%2At%5B1%5D
r%5B1%5D+=+s+-+c
d%5B1%5D+=+%28s+-+c%29%2At%5B1%5D
with the current:
d%5B2%5D+=+r%5B2%5D%2At%5B2%5D
r%5B2%5D+=+s+-+c
d%5B2%5D+=+%28s+%2B+c%29%2At%5B2%5D
-------------------------
given:
d%5B1%5D+=+5 mi
d%5B2%5D+=+5 mi
c+=+4 mi/hr
t%5B1%5D+=+t%5B2%5D+%2B+20%2F60 hr (20 min is 20/60 of an hour)
--------------------------
Now I can write:
(1) 5+=+%28s+-+4%29%2A%28t%5B2%5D+%2B+1%2F3%29
(2) 5+=+%28s+%2B+4%29%2At%5B2%5D
I have 2 equations and 2 unknowns, so it should be solvable
Since both (1) and (2) = 5, I'll set the right sides
equal to eachother
%28s+-+4%29%2A%28t%5B2%5D+%2B+1%2F3%29+=+%28s+%2B+4%29%2At%5B2%5D
Divide both sides by t%5B2%5D
%28s+-+4%29%2A%281+%2B+%281%2F3%29%2Ft%5B2%5D%29+=+s+%2B+4
s+-+4+%2B+%28s%2F3%29%2Ft%5B2%5D+-+%284%2F3%29%2Ft%5B2%5D+=+s+%2B+4
%28s%2F3+-+4%2F3%29%2Ft%5B2%5D+=+8
s%2F3+-+4%2F3+=+8t%5B2%5D
s+-+4+=+24t%5B2%5D
t%5B2%5D+=+%28s+-+4%29%2F24
Substitute this value of t%5B2%5D into (2)
(2) 5+=+%28s+%2B+4%29%2At%5B2%5D
(2) 5+=+%28s+%2B+4%29%28s+-+4%29%2F24
s%5E2+-+16+=+120
s%5E2+=+136
s+=+11.66
Her boat will go 11.66 mi/hr in still water
check answer:
(2) 5+=+%28s+%2B+4%29%2At%5B2%5D
(2) 5+=+%2811.66+%2B+4%29%2At%5B2%5D
5+=+15.66t%5B2%5D
t%5B2%5D+=+5%2F15.66
t%5B2%5D+=+.319hrs
t%5B1%5D+=+t%5B2%5D+%2B+20%2F60
t%5B1%5D+=+.319+%2B+.333
t%5B1%5D+=+.653hrs
------------------------
(1) 5+=+%28s+-+4%29%2A%28t%5B2%5D+%2B+1%2F3%29
5+=+%2811.66+-+4%29%2A.653
5+=+7.66%2A.653
5+=+4.998 close enough
(2) 5+=+%28s+%2B+4%29%2At%5B2%5D
5+=+15.66%2A.319
5+=+4.995 close enough
And, also t%5B1%5D should be 20 min
longer than t%5B2%5D
t%5B1%5D+-+t%5B2%5D+=+.653+-+.319
.653+-+.319+=+.334
.334%2A60+=+20.04min close enough