Traveling with the current a canoe can go 48 miles in 4 hour

Traveling with the current, a canoe can go 48 miles in 4 hours. traveling against the current, it takes 6 hours to go the same distance. find the speed of the canoe in still water.
I came up with the following linear equations:
12=x+y for speed of canoe with current
8=x-y for speed of canoe against current
I solved for each variable and came up with x=10, y=2.

Solution

D=RT OR R=D/T
R=48/4=12 MPH WITH THE CURRENT.
R=48/6=8 MPH AGAINST THE CURRENT
(12-8)/2=4/2=2 MPH IS THE RATE OF THE CURRENT.
PROOF:
12-2=10 MPH SPEED OF THE CANOE IN STILL WATER.
8+2=10 DITTO.