Systems of Equations Difficult Word Problem

[SovereignPariah]

A canoeist travels 20 miles down a river and back in 8 hours (40 mile round trip). She can paddle 5 miles down the rive in the same time that she can paddle 3 miles up the river. Find her rate in still water and the rate of current.

Now, the problem I have is that I seem to be missing a variable to solve the question.

time = rate X distance
b = rate in still water
c = rate of current
Downstream: is 20 = (b+c)t1
Upstream: is 20 = (b-c)t2
20/(b+c) + 20/(b-c) = 8
t1 + t2 = 8
3/(b-c) = 5 /(b+c)

Above is what I think I know about the question. I can't seem to bring it together to find the answers. I know the answer from the back of the book is b = 5.3 and c = 1.3 but I don't know how they got it. I'm probably thinking too hard. Help please.

 

[lookagain]

A canoeist travels 20 miles down a river and back in 8 hours (40 mile round trip).

She can paddle 5 miles down the rive in the same time that she can paddle 3 miles up the river.

Find her rate in still water and the rate of current.

Now, the problem I have is that I seem to be missing a variable to solve the question.

time = rate X distance


b = rate in still water


c = rate of current


Downstream: is 20 = (b+c)t1


Upstream: is 20 = (b-c)t2


20/(b+c) + 20/(b-c) = 8 \(\displaystyle \ \ \ \) <----- If this equation and the next highlighted equation are correct, ...


t1 + t2 = 8


3/(b-c) = 5 /(b+c) \(\displaystyle \ \ \ \)<----- If the previous highlighted equation and this equation are correct, ...

Above is what I think I know about the question. I can't seem to bring it together to find the answers.

I know the answer from the back of the book is b = 5.3 and c = 1.3 \(\displaystyle \ \ \)Those are rounded values,

and they are wrong without the units attached.

but I don't know how they got it. I'm probably thinking too hard. Help please.

Hint 1) Solve 3/(b - c) = 5/(b + c) for b in terms of c.



Hint 2) Wherever there is a b variable in the equation 20/(b + c) + 20/(b - c) = 8,
substitute the expression for it that you determined it equals in terms of c from the first hint.



Hint 3) Solve the equation from the second hint for c.


Hint 4) Substitute the c value back into the expression for b from the first hint.


Make sure you have the appropriate units as part of the answer, i.e. miles per hour
(or some abbreviation for it).