To find out how many mls/hour should be given, we need to first determine how many mls should be given in 1 hour.
Given that 1 liter of solution needs to be given over 10 hours, we first convert 1 liter to mls:
1 liter = 1000 mls
Next, we calculate how many mls should be given per hour:
mls per hour = Total mls / Total hours
mls per hour = 1000 mls / 10 hours
mls per hour = 100 mls/hour
Therefore, 100 mls should be given per hour.
\boxed{100 \, \text{mls/hour}}