SOLUTION: The speed of the current in a stream is 3 mi/hr. It takes a canoeist 144 minutes longer to paddle 16 miles upstream than to paddle the same distance downstream. What is the canoeis

Algebra ->  Test -> SOLUTION: The speed of the current in a stream is 3 mi/hr. It takes a canoeist 144 minutes longer to paddle 16 miles upstream than to paddle the same distance downstream. What is the canoeis      Log On


   

Question 989299: The speed of the current in a stream is 3 mi/hr. It takes a canoeist 144 minutes longer to paddle 16 miles upstream than to paddle the same distance downstream. What is the canoeist's rate in still water?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+3+ mi/hr = speed of the current
Let +s+ = the speed of the canoe in still water
+s+%2B+3+ = the speed of th canoe going downstream
+s+-+3+ = the speed of the canoe going upstream
Convert minutes to hrs:
+144%2F60+=+2.4+
---------------------------
Going downstream:
(1) +16+=+%28+s%2B3+%29%2At+
Going upstream:
(2) +16+=+%28+s-3+%29%2A%28+t+%2B+2.4+%29+
---------------------------
(1) +t+=+16+%2F+%28+s%2B3+%29+
(2) +16%2F+%28+s-3+%29+=++16%2F%28+s%2B3+%29+%2B+2.4+
Multiply both sides by +%28+s-3+%29%2A%28+s%2B3+%29+
(2) +16%2A%28+s%2B3+%29+=+16%2A%28+s-3+%29+%2B+2.4%2A%28+s-3+%29%2A%28+s%2B3+%29+
(2) +16s+%2B+48+=+16s+-+48+%2B+2.4%2A%28+s%5E2+-+9+%29+
(2) +16s+%2B+48+=+16s+-+48+%2B+2.4s%5E2+-+21.6+%29+
(2) +48+=+2.4s%5E2+-+48+-+21.6+
(2) +2.4s%5E2+=+96+%2B+21.6+
(2) +2.4s%5E2+=+117.6+
(2) +s%5E2+=+49+
(2) +s+=+7+
The canoeist's rate in still water is 7 mi/hr
check:
(1) +16+=+%28+s%2B3+%29%2At+
(1) +16+=+%28+7%2B3+%29%2At+
(1) +16+=+10t+
(1) +t+=+1.6+ hrs
and
(2) +16+=+%28+s-3+%29%2A%28+t+%2B+2.4+%29+
(2) +16+=+%28+7-3+%29%2A%28+1.6+%2B+2.4+%29+
(2) +16+=+4%2A4+
(2) +16+=+16+
OK