In 1/6 hour, 1/10 inch of snow fell.
So to find the unit rate per hour, we need to make a proportion.

1/6 is 10 minutes out of an hour so 6/6 or 1 would be an hour.
We can cross multiply. 1/10 * 1 = 1/10, 1/6 * x = 1/6x
1/6x = 1/10
Divide both sides by 1/6 to isolate x.
x = 3/5
Every hour, 3/5 inch of rain will fall.