Rational Equations: Word Problem

Question

The time it takes for a canoe to go 3 miles upstream and return is 4 hours. The

current in the lake is 1 mile per hour. Find the average speed of the canoe in still

water.

Answer 1

3=(r-1)t

3=(r+1)(4-t)

from the first equation, t=3/(r-1)

substitute into the second equation

3=(r+1)(4-[3/(r-1)])

3=(r+1)([4(r-1)-3]/(r-1)) 

multiply both sides by (r-1)

3(r-1)=(r+1)(4[r-1]-3)

3(r-1)=(r+1)(4r-4-3)

3(r-1)=(r+1)(4r-7)

3r-3=4r^2+4r-7r-7

3r-3=4r^2-3r-7

4r^2-3r-7-3r+3=0

4r^2-6r-4=0

divide both sides by 2

2r^2-3r-2=0

factor

(2r+1)(r-2)=0

r-2=0

r=2 mph is the rate of the canoe