Julies whaler cruised 45 miles upstream and 45 miles back in

Julie\'s whaler cruised 45 miles upstream and 45 miles back in a total of 8 hr. the speed of the river is 3mph. Find the speed of the boat in still water.

Solution

Let the speed of the boat in still water be \"b\"
Upstream DATA:
distance= 45; rate=b-3;time=d/r=45/(b-3)
Downstream DATA:
distance= 45; rate=b+3; time=d/r=45/(b+3)
EQUATION:
Time Up + Time Down = 8 hrs.
45/(b-3) + 45(b+3)= 8
45(b+3) + 45(b-3)=8(b^2-9)
90b=8b^2-72
8b^2-90b-72=0
4b^2-45b-36=0
b=[45-sqrt(45^2-4(4)(-36)]/8=[45-38.0657]/8=0.86678... mph
OR
b=[45+sqrt(45^2-4(4)(-36)]/8=[45+38.0657]/8=10.3832... mph