Originally Posted by

**mcruz65** The current in a stream moves at a speed of 3 mph. A boat travels 45 mi upstream and 45 mi downstream in a total time of 8 hr. What is the speed of the boat in still water?

----------- distance--- r ----t

Upstream ---- 45 mi -- r-3---t1

Downstream - 45 mi ---r+3---t2

Total Time = ----------------8 hr.

t1=45/r-3, t2=45/r+3, t1 +t2 = 8

45/r-3 + 45/r+3 = 8

Multiply both sides of the equation with (r-3)(r+3)

45(r+3)+45(r-3)=8(r-3)(r+3)

45r + 135+45r-135=8r^2-72

90r=8r^2-72

90r-90r=8r^2-90r-72

0=8r^2-90r-72

2(4r^2-45r-36)=0

2(4r + 3)(r - 12) = 0

r=12 is the only valid solution ... speed > 0