SOLUTION: Hi, I would like to just start off by saying thank you for your help. My question is as follows. A canoeist can paddle 20.0 Km down a certain river and back in 8.0 hrs. (4

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Hi, I would like to just start off by saying thank you for your help. My question is as follows. A canoeist can paddle 20.0 Km down a certain river and back in 8.0 hrs. (4      Log On


   

Question 1002245: Hi,
I would like to just start off by saying thank you for your help.
My question is as follows.
A canoeist can paddle 20.0 Km down a certain river and back in 8.0 hrs. (40.0 Km round trip). She can also paddle 5.0 km down river in the same time as she paddles 3.0 km up river. Find her rate in still water, and find the rate of the current.
Thanks again
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Look at the second part of the description first.
             rate     time    distance
DOWN         r+c       t       5
UP           r-c       t       3

system%28rt%2Bct=5%2Crt-ct=3%29
Really want a relationship between r and c.
t=5%2F%28r%2Bc%29=3%2F%28r-c%29
5%28r-c%29=3%28r%2Bc%29
5r-5c=3r%2B3c
2r-5c=3c
2r=8c
highlight_green%28r=4c%29 or highlight_green%28c=r%2F4%29


Now analyze the first part of the description.
DOWN       r+c         ()         20
UP         r-c         ()         20
TOTAL                  8          40

We can begin filling the two missing time cells.
DOWN       r+c         20/(r+c)         20
UP         r-c         20/(r-c)         20
TOTAL                  8               40

The time-sum equation should be obvious:
20%2F%28r%2Bc%29%2B20%2F%28r-c%29=8.
Try simplifying this equation before substituting either for r or for c.

I have not finished this but you should be able to.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

Hi,
I would like to just start off by saying thank you for your help.
My question is as follows.
A canoeist can paddle 20.0 Km down a certain river and back in 8.0 hrs. (40.0 Km round trip). She can also paddle 5.0 km down river in the same time as she paddles 3.0 km up river. Find her rate in still water, and find the rate of the current.
Thanks again
Speed in still water: highlight_green%2816%2F3%29 mph

Speed of current: highlight_green%284%2F3%29 mph