SOLUTION: The current in a stream moves at a speed of 4 mph. A boat travels 5 mi upstream and 13 mi downstream in a total time of 2 hr. What is the speed of the boat in still water?

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Question 876967: The current in a stream moves at a speed
of 4 mph. A boat travels 5 mi upstream and 13 mi downstream
in a total time of 2 hr. What is the speed of the boat in still water?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = the speed of the boat in still water
Going upstream:
(1) +5+=+%28+s+-+4+%29%2At%5B1%5D+
Going downstream:
(2) +13+=+%28+s+%2B+4+%29%2At%5B2%5D+
and
(3) +t%5B1%5D+%2B+t%5B2%5D+=+2+
-----------------------
(1) +t%5B1%5D+=+5+%2F+%28+s+-+4+%29+
and
(2) +t%5B2%5D+=+13+%2F+%28+s+%2B+4+%29+
-------------------------
By substitution:
(3) +5+%2F+%28+s+-+4+%29+%2B+13+%2F+%28+s+%2B+4+%29+=+2+
Multiply both sides by +%28+s+-+4+%29%2A%28+s+%2B+4+%29+
(3) +5%2A%28+s+%2B+4+%29+%2B+13%2A%28+s+-+4+%29+=+2%2A%28+s%5E2+-+16+%29+
(3) +5s+%2B+20+%2B+13s+-+52+=+2s%5E2+-+32+
(3) +2s%5E2+-+18s+=+0+
(3) +s%5E2+-+9s+=+0+
(3) +s%2A%28+s+-+9+%29+=+0+
(3) +s+=+9+
The speed of the boat in still water in 9 mi/hr
--------------
check:
(1) +5+=+%28+s+-+4+%29%2At%5B1%5D+
(1) +5+=+%28+9+-+4+%29%2At%5B1%5D+
(1) +t%5B1%5D+=+1+
and
(2) +13+=+%28+s+%2B+4+%29%2At%5B2%5D+
(2) +13+=+%28+9+%2B+4+%29%2At%5B2%5D+
(2) +t%5B2%5D+=+1+
and
(3) +t%5B1%5D+%2B+t%5B2%5D+=+2+
(3) +1+%2B+1+=+2+
OK