Kate has to fill 52 balloons for the party. Each balloon holds 5 gallons of air. For the first 10 minutes, she can fill the balloons at a rate of 8 gallons of air per minute. For the next five minutes, she fills them at half that rate. After that, she fills the rest of the balloons at a rate of 2 gallons of air per minute. How many minutes will it take her to fill all of the balloons?
She needs to fill a total of 52 * 5 = <<52*5=260>>260 gallons of air.
In the first ten minutes, she fills 8 * 10 = <<8*10=80>>80 gallons of air.
For the next five minutes, she fills 8 / 2 * 5 = <<8/2*5=20>>20 gallons of air.
That leaves her with 260 - 80 - 20 = <<260-80-20=160>>160 gallons of air to fill.
It will take her 160 / 2 = <<160/2=80>>80 more minutes to fill the rest of the balloons.
The total time to fill all of the balloons is 10 + 5 + 80 = <<10+5+80=95>>95 minutes.
#### 95