Calculus Rates Problem name________________________

The rate at which Jake uses water in his home is measured in gallons. The usage rate at Jake’s house is modeled by the function:

for

where W is the rate at which water is being used in gallons per minute and t = hours. He has a sprinkler that uses 20 gallons per hour continuously while it is in use. W does not include the water used by his sprinkler. The rate water is used by his sprinkler is defined by the function:

.

where S is the rate at which the sprinkler is using water in gallons per hour while it is in use.

a) To the nearest whole number, how much water is used at Jake’s house in one full day(24 hours)?

b) If the amount of water used during any 3 hour period exceeds 74 gallons, then there is a fine due to overuse. Is Jake’s household in compliance with this requirement? If not, what is the interval that will cause him to have a fine?

c) Jake wants to turn on his sprinkler every day for 2 hours. When should he do this so that he doesn’t go over the 74 gallon limit in 3 hours?

d) What is the average rate that water is used from 6:00 pm to 9:00 pm (t = 18 to t = 21)?