I need help w/ a difficult word problem?

Question

A sailboat travels 20 mi. downstream in 3 hrs. It returns in 4 hrs. Find the speed of the sailboat in still water AND the rate of the current.

This is how I set it up:

rate x time= distance
Downstream: r+c * 3 = 20
Upstream: r-c * 4 = 20



What do I do now?

Answer 1

Be careful with your grouping. It should be:

(r+c)*3 = 20
(r-c)*4=20

Since both left sides equal 20 -- they must equal each other, so you get:

3r+3c = 4r-4c

A little algebra gives you:

r = 7c

Now go back to either of the original equations and find c

3r+3c = 20

so
3*(7c) +3c = 20

21c+3c = 20
24c = 20

c = 20/24 = 5/6

Now that you have c -- put it into the original equation and find r.

Answer 2

3(r+c)=4(r-c)

3r+3c=4r-4c add 4c to both sides
3r+7c=4r subtract 3r from both sides
7c=r
Now you know that the current is 1/7 of the rate. So...
3(7c)+3c=20
24c=20
c=20/24 = .8333333333
multiply c by 7 to get r = 5.833333333

now try it out, if r = 5.83 mph and c=.833333, then r+c = 6.6666666

6.66666*3 = 20

r-c = 5
5*4=20

Answer 3

aint got a clue