A child watches TV at least one hour each day for 7 weeks but not more than 11 hours in any one week. Prove there is some period of consecutive days where the child matches exactly 20 hours of TV. (Assume a whole number of hours of TV is watched each day.)

A child watches TV at least one hour each day for 7 weeks but not more than 11 hours in any one week. Prove there is some period of consecutive days where the child matches exactly 20 hours of TV. (Assume a whole number of hours of TV is watched each day.)