October 26, 2009
1.
You are driving along a straight highway where the speed limit is 65 miles per hour. You pass a highway
patrol car sitting 1000 feet from the highway on your left. Thirtyﬁve seconds later, the highway patrolman
checks his radar to see if you are speeding. His radar tells him that the distance between you and him is
3000 feet and that the distance between you and him is increasing at a rate of 95 feet per second. Since 95
feet per second equals approximately 64.77 miles per hour, the highway patrolman decides that you are not
speeding. Is the highway patrolman’s decision correct? How fast are you actually driving?
2.
A water tank has the shape of an inverted circular cone with base radius 6 feet and height 12 feet. If
water is being pumped into the tank at a rate of 10 cubic feet per minute, ﬁnd the rate at which the water
level is rising when the water is 5 feet deep.
1
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 Fall '09
 BenedictGross
 Math, Imperial units, ScoobyDoo, Miles per hour, Shaggy, highway patrolman

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