A Math Story Problem for Adults, Sep07


It’s that time of year when many adults are headed back to college. These brave souls often find they need remedial help with math. The following is offered as a study aid, for the mature student.

At 6 p.m. Bart boards a train headed due east for Hooterville. Exactly 45 minutes later, his sister Glenda boards a train headed due north, for Bentonsport. If both trains travel at exactly the same speed, and the distance as the crow flies between Hooterville and Bentonsport is 65 miles, how fast are the trains going? At midnight, the engineer of one train falls asleep, taking his foot off the pedal, and his train begins to slow to half its original speed. Since the engineer on the other train has taken a stimulant, in his nervous excitement he increases the speed of his train by 25 percent. Which train will crash? When? If the engineers survive the crash, which one will lose his job? Why?

Barb waits 2.5 hours for her husband Grant to come home from work. When he does arrive, he is 3.2 hours late. If Grant was carrying 14.5 grams of cocaine in his pocket, and if the original packet he purchased on the street weighed 30.75 grams, how many grams per hour did Grant consume after work? Was Grant already high when his wife started waiting for him? If cocaine wears off at the rate of 40 percent per hour, when he walks through his front door is Grant still at least half as high as he was when he first ingested the drug?

Bobby and Grant share an apartment in a decrepit neighborhood downtown. There they take drugs and consort with a variety of women. The rent on this apartment is $245 per month (utilities included). Bobby is on parole for an earlier drug-related felony, and if caught again faces up to 20 years in prison. If he is caught, and his annual salary is $55,000 a year, how much per month will his share of the apartment ultimately cost him?

It so happens that Bobby and Grant see the same psychoanalyst, Monica. Her office is on the fourth floor of a medical building. Monica received her doctorate 5 years ago, and has been paying back an $80,000 student loan at the rate of $7,000 per year. Fortunately, the interest rate on that loan is only 2 percent. Assuming she works 38 hours a week, and the overhead for her office consumes 35 percent of her gross income, how much will she have to charge per hour to make a net income of $60,000 per year?

Monica has Grant on 20 mg of Paxil per day, whereas Bobby takes 300 mg of Wellbutrin. In his therapy sessions, Bobby admits that he is having an affair with Barb, his friend Grant’s wife. Monica seems unimpressed. This lack of disapproval excites Bobby, and his blood pressure rises 10 points. It also makes Bobby think about having sex with Monica. When Grant sees Monica, he spends most of his time complaining about how lonely he feels, and how bored he is in his marriage to Barb. Sometimes he cries, emitting tears at the rate of 12 per minute.

During the 50-minute sessions, Grant has 1 major breakthrough and 4 significant revelations. Bobby rarely learns anything from his sessions, but enjoys them anyway, as they give him a chance to brag about his conquest of Barb, and to plot his affair with Monica.

If Bobby and Barb were free to marry, how many weeks would their marriage last?

If Monica and Grant were to marry, how long would their marriage last? (Hint: Monica is gay.)

At 1:15 p.m. the police raid Bobby and Grant’s apartment. No one is home at this hour, and they find 2.3 grams of cocaine on the coffee table. When Bobby arrives, 23 minutes later, they arrest him. They inform him that mandatory minimum sentencing laws require that if convicted of a felony, he will go to jail for at least 20 years. They offer him a deal. If he will narc on Grant, they will reduce the charge to an aggravated misdemeanor.

Grant arrives at the apartment at 3:05 p.m., and is pleasantly surprised to find Bobby already there, holding a rock of 93 percent pure cocaine. But before they can light up the crack pipe, Grant notices that there is something artificial in Bobby’s behavior. Rather than stick around for the bust, Grant jumps into his car and heads due West to Hooterville, driving at the average speed of 75 miles per hour. Exactly 2 minutes later, the police crash through the door, and then jump into their car, heading east at an average speed of 90 miles per hour. How many minutes does it take for the police to realize they’re headed in the wrong direction? If the police try to turn around and race back the way they came, how long until they reach the train headed to Hooterville? Is that the train operated by the sleepy engineer, or the speedy one?

Did Bart and Glenda ever meet? If not, why?

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