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) (Show Source): You can put this solution on YOUR website!
Let = the speed she can paddle in still water in km/hr
= the speed of the kayak going downstream in km/hr
= the speed of the kayak going upstream in km/hr
Let = her time in hrs to travel 15 km upstream
= her time in hrs to travel 15 km downstream
----------------------------------------------------
Her equation for paddling upstream:
(1)
Her equation for paddling downstream:
(2)
---------------------------------
(2)
and
(1)
Substitute (1) into (2)
(2)
(2)
Multiply both sides by
(2)
(2)
(2)
(2)
Use the quadratic formula
The speed she can paddle in still water is 8 km/hr
check:
(1)
(1)
(1) hrs
and
(2)
(2)
(2)
(2)
(2) hrs
OK
Answer by stanbon(75887) (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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