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WASHINGTON STATE MATHEMATICS COUNCIL 2001 MIDDLE SCHOOL MATH OLYMPIAD Session I: SEVENTH/EIGHTH GRADE PROBLEM SOLVING |
7-8 |
In
case of an emergency radiation leak at a nearby nuclear power plant, the
manager is setting up a phone tree to call 10,000 homes in 15 minutes. In round
1, the manager calls 3 homes. In round 2, the person called in each of the 3
homes calls 3 more homes, who then each call 3 additional homes, and so on
until all 10,000 homes have been called. This is called a 3-person phone tree. The
manager starts calling at 10:21 and the phone tree must reach all homes in 15
minutes.
A community member is
concerned that this may take too long and proposes a 5-person phone tree. The
manager would call 5 homes and each person in turn would call 5 more homes and
so on. The community leaders want to
know:
1. Will the 3-person phone tree work for the current 10,000 homes?
2. Will the 3-person phone tree work for a future population of 50,000 homes?
3. Will the 5-person phone tree be needed now (with 10,000 homes) or in the future (with 50,000 homes)?
4. Would a different phone tree plan work better for the current and future population?
1. Table or Diagram:
For the 3-person phone tree plan, the 5-person phone tree plan, and one other phone tree plan of your
choosing, draw a table or diagram showing how many rounds of calls must
be made before all homes are contacted, and explain how you came up with the
figures. You need to figure out how many calls, total, have been made at the end of each round.
·
Assume that the
manager starts the first call at 10:21 am.
·
Assume that each call
lasts 1 minute, including dialing time.
·
Assume that the next
round of phone calls does not begin until all homes have been contacted during
the current round.
2.
Exact Time
Needed for Each Plan: For the 3-person plan, the 5-person plan,
and the phone tree plan of your
choosing, you must state exactly how long it will take to reach all the
homes.
Prepare
a report for the community leaders. In this report you must:
·
State your
understanding of your assignment.
·
Summarize your
findings about the two proposed plans for contacting the current 10,000 homes
and the possible future plan for 50,000 homes.
·
Summarize your
findings about the phone tree plan of
your choosing, and state your reasons for trying this phone tree plan.
·
State your
recommendation: Should they use a 3-person tree? Should they use a 5-person tree? Should they use your alternative
phone tree plan? What is your
recommendation for this community considering its current and future population
needs?
·
Support your
recommendation with your reasoning based on your findings.
·
Your Answer(s).
·
Your Understanding of
the Problem.
·
Your Strategies Used.
·
Your Communication.
· Your Reasonableness/Reasoning