SOLUTION: John paddled his kayak 10km upstream against a 3km/hr current and back again in 3.5 hours. Find his paddling rate in still water.

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Question 568900: John paddled his kayak 10km upstream against a 3km/hr current and back again in 3.5 hours. Find his paddling rate in still water.
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
Kayak speed x km/h
current speed 3 km/h

against current x-3 km/h
with current x+3 km/h

Distance= 10 km

Time against + time with = 3.5 hours
t=d/r
10 /( x + 3 ) + 10 /(x - 3 ) = 3.5

LCD = (x - 3 ) ( x + 3 )
10 *( x - 3 ) + 10 (x + 3 ) = 3.5
10 x - 30 + 10 x + 30 = 3.5 ( x ^2 - 9
20 x = 3.5 x ^2 -31.50
3.5 x ^2 -20 x -31.5

Find the roots of the equation by quadratic formula

a=3.5, b=-20, c=-31.5

b^2-4ac=400+448
b^2-4ac=848
sqrt%28848%29=29.12
x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29
x1=-b%2Bsqrt%28b%5E2-4ac%29%29%2F%282a%29
x1=(20+29.12)/7
x1=7.02
x2=(20-29.12)/7
x2=-1.3
Ignore negative
CHECK
10/(7+3)+10/(7-3)= 3.5
m.ananth@hotmail.ca