For 1 hour on a rainy day, Ken can cycle 3*30=90 miles.
For 1 hour on a snowy day, Ken can cycle 3*10=<<3*10=30>>30 miles.
On the rainy days this week, Ken cycled 90*3=<<90*3=270>>270 miles.
On the snow days of the week, Ken cycled 30*4=<<30*4=120>>120 miles.
In total, Ken cycled 120+270=<<120+270=390>>390 miles this week.
#### 390