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?
Thoughts? Step-by-step reasoning:
She needs to fill a total of 52 * 5 = 260 gallons of air. In the first ten minutes, she fills 8 * 10 = 80 gallons of air. For the next five minutes, she fills 8 / 2 * 5 = 20 gallons of air. That leaves her with 260 - 80 - 20 = 160 gallons of air to fill. It will take her 160 / 2 = 80 more minutes to fill the rest of the balloons. The total time to fill all of the balloons is 10 + 5 + 80 = 95 minutes.
Thus, the answer is 95.