Math 141, Sem. I, 1998-99 (R.A. Brualdi) Handout 5 (September 17, 1998) Topic: Constant Rate Problems 1. [Take the distance between Madison and Chicago to be 150 miles.] Suppose you drive from Madison to Chicago at a constant speed of 70mph and return at a constant speed of 50 mph. Determine the average speed for the round trip? 2. [Take the distance from Madison to Beloit to be 50 miles, and so the distance from Beloit to Chicago to be 100 miles.] Suppose you drive from Madison to Chicago via Beloit. From Madison to Beloit you travel at a constant speed of 55 mph. (a) At what constant speed should you travel from Beloit to Chicago if you want an average speed of 60 mph? At what constant speed should you travel from Beloit to Chicago if you want the total time from Madison to Chicago to be 2 1/2 hours? 3. A lizard runs at 3.5 mph during daylight hours [taken to be 6 AM to 6 PM in this problem] and 1.0 mph during nighttime [6 PM to 6 AM]. A porcupine always runs at 2.0 mph. If the lizard and the porcupine start from the same place at noon, does the porcupine catch up to the lizard and, if so, when? 4. If the race is run later in the year when daylight hours are 5 AM to 7 PM, and if the race is started at sun-up (5 AM), does the porcupine catch the lizard and, if so, when? 5. Water is leaking into a boat you are in at the rate of one gallon every two minutes. Already 40 gallons have leaked in and you are now getting worried. If you pump water out at a rate of 3 gallons per minute, how long will it take you to pump the boat dry? How fast would you have to pump water out to get the boat dry in 8 minutes? 6. The Water Utility of a town figures that the town residents use water at two different rates: -- From 6 AM to 9 PM, the average town use is 1600 gallons per minute. -- From 9 PM to 6 AM, it is 400 gallons per minute. To even out the work on the town pumps, there is a water tower into which water is pumped in at a constant rate 24 hours a day. This rate is chosen so that water is pumped in faster than it is used during night hours [9 PM to 6 AM] but runs out faster than it is pumped in during day hours [6 AM to 9 PM], and at the end of 24 hours, there is just as much water in the tank as the previous day. How fast is the water pumped in? How large a tank does the town need?