# How do I write a system of two equations in two variables to solve this problem?

A Mississippi riverboat travels 30 miles downstream in three hours and then makes the return trip upstream in five hours. Find the speed of the riverboat in still water and the speed of the current.

riverboat in still water ____ mph

current _____ mph

Relevance
• 8 years ago

Call s1= speed of riverboat

s2= speed of current

We have system of linear equation:

(1) (s1 + s2)*3=30 (this is because of the formula: distance=speed*time)

(2) (s1 - s2)*5=30 (when you go opposite the river, the speed of current reduce the speed of the boat and in order to be able to go the opposite direction, your speed of boat must be larger, that is why I write s1-s2.)

Solve this we got,s1=8 mph s2=2 mph

The speed of the boat is 8 mph

of current is 2mph

Best luck in your study !

• 8 years ago

Downstream it goes 10 mph, upstream it goes 6 mph. So with no current it goes 8 mph. And the current is going 2 mph. That's all I can find out