# River boat round trip

A river boat can travel at $20$ km per hour in still water. The boat travels $30$ km upstream against the current then turns around and travels the same distance back with the current. If the total trip took $7.5$ hours, what is the speed of the current? Solve this question algebraically as well as graphically.

• Welcome to MSE. What have you tried? Here are some hints: Name some variables. Write down some equations in those variables that amount to distance $=$ rate $\times$ time. – Sammy Black Apr 17 '13 at 22:43

Hint: if the current is $c$, the speed upstream is $20-c$ and downstream is $20+c$
$x=(v_{\rm still}-v_{\rm current})t_1$ (when it goes upstream)
$x=(v_{\rm still}+v_{\rm current})t_2$ (when it comes back downstream)
$t_1+t_2=7.5$
and solve for $v_{\rm current}$ , you know the rest of the variables.