SOLUTION: Stephanie took her kayak to the kaweak river, which flows downstream at a rate of 2 kilometers per hours. She paddled 15 km upstream, and then paddle downstream to her starting po

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Question 1010003: Stephanie took her kayak to the kaweak river, which flows downstream at a rate of 2 kilometers per hours. She paddled 15 km upstream, and then paddle downstream to her starting point. If this round trip took a total of 4 hours, find the speed that Stephanie can paddle in still water.
Found 2 solutions by josmiceli, stanbon:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = the speed she can paddle in still water in km/hr
+s+%2B+2+ = the speed of the kayak going downstream in km/hr
+s+-+2+ = the speed of the kayak going upstream in km/hr
Let +t+ = her time in hrs to travel 15 km upstream
+4+-+t+ = her time in hrs to travel 15 km downstream
----------------------------------------------------
Her equation for paddling upstream:
(1) +15+=+%28+s+-+2+%29%2At+
Her equation for paddling downstream:
(2) +15+=+%28+s+%2B+2+%29%2A%28+4+-+t+%29+
---------------------------------
(2) +15+=+4s+%2B+8+-+%28+s+%2B+2+%29%2At+
and
(1) +t+=+15%2F%28+s+-+2+%29+
Substitute (1) into (2)
(2) +15+=+4s+%2B+8+-+%28+s+%2B+2+%29%2A%28+15%2F%28+s+-+2+%29+%29+
(2) +7+=+4s+-++%28+s+%2B+2+%29%2A%28+15%2F%28+s+-+2+%29+%29+
Multiply both sides by +s+-+2+
(2) +7%2A%28+s+-+2+%29+=+4s%2A%28+s+-+2+%29+-+15%2A%28+s+%2B+2+%29+
(2) +7s+-+14+=+4s%5E2+-+8s+-+15s+-+30+
(2) +4s%5E2+-+30s+-+16+=+0+
(2) +2s%5E2+-+15s+-+8+=+0+
Use the quadratic formula
+s+=+%28-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+2+
+b+=+-15+
+c+=+-8+
+s+=+%28-%28-15%29+%2B-+sqrt%28+%28-15%29%5E2+-+4%2A2%2A%28-8%29+%29%29+%2F+%282%2A2%29+
+s+=+%28+15+%2B-+sqrt%28+225+%2B+64+%29%29+%2F+4+
+s+=+%28+15+%2B-+sqrt%28+289+%29%29+%2F+4+
+s+=+%28+15+%2B+17+%29+%2F+4+
+s+=+32%2F4+
+s+=+8+
The speed she can paddle in still water is 8 km/hr
check:
(1) +15+=+%28+8+-+2+%29%2At+
(1) +15+=+6t+
(1) +t+=+2.5+ hrs
and
(2) +15+=+%28+8+%2B+2+%29%2A%28+4+-+t+%29+
(2) +15+=+10%2A%28+4+-+t+%29+
(2) +15+=+40+-+10t+
(2) +10t+=+25+
(2) +t+=+2.5+ hrs
OK

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Stephanie took her kayak to the kaweak river, which flows downstream at a rate of 2 kilometers per hours. She paddled 15 km upstream, and then paddle downstream to her starting point. If this round trip took a total of 4 hours, find the speed that Stephanie can paddle in still water.
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Upstream DATA::
distance = 15 km ; rate = b-2 mph ; time = 15/(b-2) hrs
----
Downstream DATA:
distance = 15 km ; rate = b+2 mph ; time = 15/(b+2) hrs
-----
Equation:
time + time = 4 hrs
15/(b-2) + 15/(b+2) = 4
15(b+2) + 15(b-2) = 4(b^2-4)
30b = 4b^2 - 16
-----
2b^2 - 15b - 8 = 0
-----
Factor::
2b^2 - 16b+ b - 8 = 0
-----
2b(b-8) + b-8 = 0
-----
(b-8)(2b+1) = 0
Positive solution::
boat speed = 8 km/hr
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Cheers,
Stan H.
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