pre algebra word problem

Question

A boat traveled 36 miles downstream and back. The trip downstream took 2 hours. The trip back took 3 hours. Find the speed of the boat in still water and the speed of the current.

Answer 1

So first you analyze the problem. You know you're dealing with a two variable problem, because they asked you to find two things. Let's call our two variables x and y. So now we have to figure out what x and y are. We do this by setting up and solving equations. The number of equations must be equal to the number of variables to solve. So what do we know?

Well...we went downstream first. So that means we get the speed of us rowing plus the speed of the current right? There's your fun fact on downstream vs upstream too. You'll need to know that for changing oxygen sensor's on cars too. But whatever. Anyway.

 

Ok so our two variables x and y. Let's name them. x will be us, because...well because I said so. y will be the speed of the current, because we already named x and we only have one variable left. Or because I said so. It all adds up. Anyway.

So we know the speed of us paddling plus the speed of the stream equals the speed of us going downstream. So...

x + y = What?

I don't know because I don't have any speeds given to me. But I do know that I went 36 miles in 2 hours right? Which would be how fast? Do it in miles per hour or miles/hours or mi/hr. So that would look like...

 

36miles/2 hours = 18mi/hr

 

Ok so we have a speed. 18 mi/hr. Now plug that in as how fast you were going.

 

x + y = 18mi/hr

But that's one equation and I have two variables, so I can't solve it. So I need another. Well for the trip back I went the same distance right? 36 miles, but it took me a little longer because I had to fight the current, so 3 hours. So I can now calculate the speed that I went upsteam. 

36miles / 3 hourse = 12 mi/hr

 

So now I know that I'm rowing upstream, which means that I'm still pushing the boat forward, but the current is pushing against me. So x is positive and y is negative. It looks like this.

 

x + y = 12mi/hr

 

So now I have two equations. All I have to do is solve. I would assume you know how to do that from your class notes or book. Good luck! If you have any more questions, feel free to message me.

Thanks,

Mat S.