Please help me understand the direction in which Frodo and company first set out from Shire
In the chapter "Three is company"
"For a short way they followed the lane westwards. Then leaving it they turned left and..."
Then the next paragraph - "After some time they crossed the Water, west of Hobbiton"
These sentences have me confused. In the accompanying maps, North is on the top of the map, i.e., Hobbiton is to the North of Shire.
What is the path they have taken?