SOLUTION: Jan and Tariq took a canoeing trip, traveling 6 mi upstream against a 2 mi/h current. They then returned to the same point downstream. If their entire trip took 4 h, how fast can t

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: Jan and Tariq took a canoeing trip, traveling 6 mi upstream against a 2 mi/h current. They then returned to the same point downstream. If their entire trip took 4 h, how fast can t      Log On

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Question 422234: Jan and Tariq took a canoeing trip, traveling 6 mi upstream against a 2 mi/h current. They then returned to the same point downstream. If their entire trip took 4 h, how fast can they paddle in still water? [Hint: If r is their rate (in miles per hour) in still water, their rate upstream is r - 2 and their rate downstream is r + 2.]
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
speed in still water = r
current speed 2

upstream speed = r-2
downstream speed = r+2

Distance= 6 miles

Time upstream + time downstream = 4 hours
t=d/r
6/(r+2)+ 6/(r-2)= 4
LCD =(r- 2)(r+2)
6*(r-2) +6(r+2)= 4
6r-12+6r +12=4(r^2-4)
12r=4r^2 -16
4r^2-12r -16=0
4(r^2-3r-4)=0
(r^2-3r-4)=0

Find the roots of the equation by quadratic formula
a= 1 , b = -3 , c = -4 .
b^2-4ac= 25
x1=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29
x1=%283%2Bsqrt%2825%29%29%2F2
x1=4
x2=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29
x2=%283-sqrt%2825%29%29%2F2
x2=-1 ( this is negative so not possible)
The speed of paddling in still water = 4 mph