Charlie and LaQuanda plan to meet at the railroad station to take the train that leaves at 8:00. Charlie thinks his watch is 25 minutes fast, but it is really 10 minutes slow. LaQuanda thinks her watch is 10 minutes slow, but it is really 5 minutes fast. Each one looks only at his/her own watch. The two plan to meet each other at the station at 7:55. What happens?
Solution
Discussion: Problems like this can get one tangled up in all the confusing information, which is exactly why we do them. It is necessary to suspend one's immediate characterization of Charlie and LaQuanda as idiots who don't know how to take care of their watches and who also don't know how to look at a clock. (I rant further about this sort of thing in #2440.15: the rocket sled.)
Solving the Problem: We can begin by working out Charlie's situation, and then LaQuanda's. A chart will help, or simply a list--anything to get the information into some sort of clear display. Here's a sample solution in list format:
• Charlie wants to arrive at 7:55.
• He thinks his watch will say 8:20 at that time (because he thinks it's 25 minutes fast).
• But the time then is actually 8:30 (because it's really 10 minutes slow).
• So he misses the train.
• LaQuanda wants to arrive at 7:55.
• She thinks her watch will say 7:45 then (if it's 10 minutes slow).
• But the time is really 7:40 (because it's 5 minutes fast).
• So she is early and makes the train.
Heuristics: #3: make charts and tables (or careful lists) of the information you have or can generate. There's a little bit of #8: act it out here, too, as you follow the steps in their minds.
Using the Problem with Students:
a. as an overnight assignment. Once the problem is read, I simply throw it into the class's lap, at least for awhile. I am entirely up-front about the stupidity of the problem, as in the discussion above, and might also encourage some dramatic background--why are they meeting at the train? Is it 8:00 am or pm? Imagination is always to be encouraged.
After the students have worked on it for as long as you think right, whether it's in class or overnight, it's time to work it out carefully. This is usually a rather intense discussion, where the class needs to understand each of the steps as in the solution presented above.
And, once again, there's drama: What does LaQuanda do when she realizes Charlie isn't going to make it? Does she get on the train herself? Does she call him on his cell phone? What does she say?
Modifying or Extending the Problem: You can reflect on the numbers involved: Charlie's are 25 and 10, and he's 35 minutes late. LaQuanda's are 10 and 5, and she's 15 minutes early. What's going on here?