Mario paddled his canoe upstream for 3 hours. When he turned around and paddled back to his starting point it only took 1 hour. if the river flows at at a speed of 3 miles per hour, how fast could Mario paddle his canoe in still water?
a) 1mph b) 2mph c) 3mph d) 6mph e) 9mph

Question

Mario paddled his canoe upstream for 3 hours. When he turned around and paddled back to his starting point it only took 1 hour. if the river flows at at a speed of 3 miles per hour, how fast could Mario paddle his canoe in still water?
a) 1mph  b) 2mph  c) 3mph  d) 6mph  e) 9mph

whpalmer4 · Answer

$$d = rt$$

We know that the distance upstream and downstream is identical.  His speed upstream will be $$r_u = r_s - r_r$$ and his speed downstream will be $$r_d = r_s + r_r$$ where $r_s$ is his speed in still water, $r_r$ is the speed of the river, and $r_u$ is his speed upstream.

distance upstream =$ 3*r_u$ = distance downstream =$1*r_d$

$$3*r_u = r_d$$Substitute in our expressions for the upstream and downstream speeds:
$$3*(r_s-r_r) = (r_s + r_r)$$We know the value of $r_r = 3$ so you should be able to solve for the value of $r_s$.

anonymous · Answer

so it will be (r-3)=(r+3)?

whpalmer4 · Answer

$$3*(r_s - r_r) = (r_s + r_r)$$$$3*(r_s-3) = (r_s+3)$$$$3r_s - 9 = r_s + 3$$$$r_s = $$

anonymous · Answer

=6

whpalmer4 · Answer

Yep, but let's check the answer.

paddling upstream, against current, he has a net speed of 6-3 = 3 mph.  It takes him 3 hours, so he goes 9 miles.  Downstream, he has a net speed of 6+3 = 9 mph.  Therefore in the 1 hour he paddles downstream, he goes 9 miles.  That's the same distance in each direction, so the answer checks.

whpalmer4 · Answer

You'll see this sort of construction often — airplanes flying with or against the wind, boats in currents, etc.

whpalmer4 · Answer

Because it was written in terms of a fraction of the distance instead of a number of miles, the actual distance didn't matter in the solving of the equation.

anonymous · Answer

oh, ok :) i understand it now. thank you for your help!

whpalmer4 · Answer

I've always enjoyed solving these problems - it seems like an impossible task at first, and then a minute later, you have the answer  :-)

anonymous · Answer

ya word problems are not my favorite. but i do understand it now, its a great help because my elm test is tomorrow :)

whpalmer4 · Answer

good luck with that!  if you want to get better at word problems, there's a good book by a woman named Mildred Johnson called How to solve word problems in Algebra.  Look for it at your library or bookstore.  She goes through all the usual kinds of word problems and shows you how to systematically solve them.

whpalmer4 · Answer

work through the book and you'll be the person all your friends ask for help with their word problems :-)