SOLUTION: Please help me set up this problem: "Tim paddled his kayak 12 km upstream against a 3 km/hour current and back again in 5 hours and 20 minutes. In that time how far could he hav

Algebra ->  Rational-functions -> SOLUTION: Please help me set up this problem: "Tim paddled his kayak 12 km upstream against a 3 km/hour current and back again in 5 hours and 20 minutes. In that time how far could he hav      Log On


   

Question 427563: Please help me set up this problem:
"Tim paddled his kayak 12 km upstream against a 3 km/hour current and back again in 5 hours and 20 minutes. In that time how far could he have paddled in still water?"
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!

speed in still water = r
current speed =3

upstream speed = r-3
downstream speed = r+3

Distance= 12 miles

Time upstream + time downstream = 5.33 hours
12/(r+3) +12/(r-3 )=5.33
LCD = (r-3)(r+ 3)
12*(r-3) +12(r+3 )= 5.33
12r-36r+12r+36=5.33
r^2-24r=5.33r^2-47.97
5.33r^2- 24r-47.97
Find the roots of the equation by quadratic formula
a=5.33 b=-24 c=-47.97
b^2-4ac= 576+1022.72
b^2-4ac= 1598.72
x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29
x1=%28-b%2Bsqrt%28b%5E2-4ac%29%29%2F%282a%29
x1=(24+ 39.98)/ 10.66
x1= 6
x2=(24-39.98) /10.66
x2= -1.5 ( ignore)
Speed = 6 mph