# Problem about a boat on a river

A boat on a river travels 20 miles downstream in only 2 hours. It takes the same boat 6 hours to travel 12 miles upstream. What are the speed of the boat and the speed of the current?

• @DanBrumleve I think the friction is neglected. Jan 26 '12 at 11:04

Let the speed of the boat be $v_b$ and the speed of the current $v_c$. When he goes downstream, his speed is $v_b+v_c$; when he goes upstream, it’s $v_b-v_c$. If he travels for $2$ hours at a speed of $v_b+v_c$ miles per hour, he’ll go $2(v_b+v_c)$ miles. You know how far he actually did go when he travelled downstream, so you should be able to find $v_b+v_c$ without much trouble. Now apply the same reasoning to the upstream leg to fine $v_b-v_c$. You will then have two very simple equations in the unknowns $v_b$ and $v_c$ that can easily be solved for these unknowns.