Question

The total time it takes for a canoe to go 3 miles upstream (against current) and back 3 miles downstream (with the current) is 4 hours. The current in the lake is 1 mile per hour. Find the speed of the canoe in still water.

Answer 1

I think you have your times backwards.
Obviously it is going to take longer to go against
the current than it takes to go with the current.
I will assume you have typo and fix it.

speed of canoe in still water --- x mph
time to go upstream = 3/(x-1)
time to go downstream = 3/(x+1)

3/(x-1) + 3/(x+1) = 4
multiply by (x^2 - 1)
3(x+1) + 3(x-1) = 4x^2 -4
4x^2 - 6x - 4 = 0
2x^2 - 3x - 2 = 0
(x - 2)(2x + 1) = 0
x = 2 or x = -1/2, rejecting the negative answer,

x = 2
The boat can go 2 mph in still water

check:
time to go against current = 3/1 = 3 hours
time to go with the current = 3/3 = 1 hour, for a total of 4 hours

Answer 2

skip the first part of my answer:
"I think you have your times backwards.
Obviously it is going to take longer to go against
the current than it takes to go with the current.
I will assume you have typo and fix it."

I forgot to delete it from my post. I had typed that after
I misread your question initially.