Question 26919
The boat has a steady rate of speed, let's call it "r" but it's total speed is being effected by speed of the current, let's call that "c".  When the boat is moving upstream, the current is fighting against the boat and is <b><i>subtracting</i></b> from its speed. Thus when moving upstream, the boat's motion is given by (30 min=.5 hr):
a) {{{(.5)(r-c)=16}}}
When it's moving downstream the boat's speed is <b><i>increased</i></b> by the current and it is given by (20 min=1/3 hr):
b) {{{(1/3)(r+c)=16}}}
To find the speed of the current, this is a good problem to use elimination. First divide 16 in your two equations by the amount of time it took to rewrite as:
{{{r-c=16/.5=32}}} &
{{{r+c=16/(1/3)=48}}}
Subtract the bottom equation from the top (since we're trying to find c, if we wanted to find r first we'd add them) to get:
{{{-2c=-16}}} Divide:
{{{c=8mph}}}