`Uncorking Work ProblemsDavid Drymiller                Marie Sklodowska Curie Metro H.S.                               4959 S. Archer Ave.                               Chicago IL 60632                               (312) 535-2120Objectives:     To solve problems about work, using the formula work = rate x time.     To solve equations containing rational expressions.     To strengthen basic skills learned in Algebra.  Materials Needed:     A large clear plastic bottle with 3 different sized holes drilled         in the bottom     3 corks to fill the holes     A plastic storage crate     A plastic container that fits into the storage crate     A plastic funnel     Stopwatches     A pliers     Rags to wipe up spills     Saran wrap     food coloring     colored strips of paperStrategy:           The students perform the following demonstration for their classmatesunder the direction of the classroom teacher.  No prior knowledge of the activity is needed by the students.     Have the students fill the bottle with water and place it on the crate. Place the container in the crate to catch the water when the bottle is drained.  Place one colored strip of paper near the top of the bottle, but below the water level.  The other strip should be placed on the bottle near,but not exactly at, the bottom.  Add food coloring to the water to make theevent easier to see.  Place a piece of Saran wrap on the top of the bottle to form a seal.  Using the pliers, remove the smallest cork.  Remove theSaran wrap and start the stopwatches when the water level reaches the topof the first colored strip.  Stop the stopwatches when the water level reachesthe top of the second colored strip.  Recork and refill the bottle.  Recordthe time it takes to empty the bottle using the smallest hole.  (I got 127seconds.)      Again drain the bottle as before but pull the middle sized cork and record the results.  (I got 65 seconds.)     Now ask the question, "How long does it take to drain the bottle if boththe smallest and middle sized corks are pulled?"     The formula, Work = Rate x Time is introduced and our discussion leads to the following chart, equation and prediction for the time.                             Rate    x     Time    =   Work           Smallest Hole     1/127         127          1           Middle Size       1/65           65          1           Both Together     1/t            t           1                1/127  +   1/65  =   1/t                65t    +   127t  =  65(127)                           270t  =  65(127)                              t  =  43 sec.     Again drain the bottle by pulling both the small and middle sized corksand record the result.  (I got 43 seconds---Perfection!)     A variation of the above can be obtained by first draining the bottle by uncorking the middle and largest holes and predicting the time needed to drain the bottle using just the largest hole.  Here some error might appear in the timing of the event. `