Part 1. The Predicament of Betsy and Bert
Betsy and her brother Bert must help with the household chores before they can go out with their friends. Their job is twofold:
A. They must wash and dry one sink full of dirty dishes that accumulated for three days.
B. They must sweep up and take out three loads of trash from the garage, which hasn’t been cleaned since the summer of 1998.
Bert and Betsy’s parents have announced that neither of them may go out until both jobs are completed. Both Bert and Betsy want to go out with their friends as soon as possible. As shown in the table, Betsy can wash two sink loads of dishes in one hour, or she can sweep up and take out three loads of trash. Bert can wash one sink load of dishes in one hour, or he can sweep up and take out one load of trash. (Assume that if Bert and Betsy work together, they still work at the pace shown in the table.) Answer the questions below to determine how Bert and Betsy can complete both jobs in the shortest amount of time.
1. Who is better at cleaning dishes: Bert or Betsy?
2. If Bert and Betsy work together, how many loads of dishes can they do in one hour?
3. How many minutes would it take for them to wash one load of dishes working together? Show how you got your answer.
4. Who is better at sweeping up and taking out trash: Bert or Betsy?
5. If Bert and Betsy work together, how many loads of trash can they do in one hour?
6. How many minutes would it take for them to sweep up and take out three loads working together? Show how you got your answer.
Part 2. Analyzing the Options
Now that you have worked with the data, it is time to use this information to make a decision. Read each of the options below. Answer the questions to determine the total amount of time it would take to complete the job of sweeping up and taking out three loads of trash and washing one sink full of dishes.
Option 1. The Parents’ Plan: Bert and Betsy’s parents suggest that they consider dividing the tasks by working together on both jobs. First they should both work on the dishes, then they should both tackle the sweeping. Betsy complains that this wouldn’t be fair because Bert is a lazy slob and won’t do his share of the work. However, she is willing to go along if this allows them to finish sooner.
Time to complete one sink full of dishes: _____________
Time to complete three loads of trash: _____________
Time it would take for both to be finished: _____________
Option 2. Betsy’s Plan: Betsy argues that they should divide up the tasks and work separately. She says she should do the dishes because she likes this job better and, besides, Bert made most of the mess in the garage so he should clean up the trash.
Time to complete one sink full of dishes: _____________
Time to complete three loads of trash: _____________
Time it would take for both to be finished: _____________
Option 3. Bert’s Plan: Bert argues that Betsy should do all the work. He suggests that this would be the most efficient option because she is so much faster and better at doing both jobs.
Time to complete one sink full of dishes: _____________
Time to complete three loads of trash: _____________
Time it would take for both to be finished: _____________
Option 4. Friend’s Plan: Betsy’s friend, who has just taken economics in school, tells them they are all wrong because each person should specialize in what he or she does best. She recommends that Betsy should do all the sweeping because, of the two jobs and compared with Bert, she is better at sweeping. Bert should do all the dishwashing because this is what he does best.
Time to complete one sink full of dishes: _____________
Time to complete three loads of trash: _____________
Time it would take for both to be finished: _____________
Which option is the most efficient: which allows Betsy and Bert to complete the job in the shortest amount of time? Explain.