COMPETITION HOMEPAGE

ONLINE REGISTRATION

PARTICIPATING TEAMS

COMPETITION RESULTS

SCHEDULE

SAMPLE TESTS

DIRECTIONS

VIRTUAL CAMPUS TOUR

MATHEMATICS DEPARTMENT

Huntington University Invitational
High School Mathematics Competition

Sample Team Test

A sample of a Team Problem Solving investigation is given below.

Harry the Hare challenges Tina the Tortoise to a race on a 20-m track. The day of the race, Tina jumps off to a quick lead, burning up the track at a blistering 0.2 m/sec. Harry the Hare, supreme in his overconfidence, remains at the starting line boasting to the crowd in the bleachers, delaying his start for an additional 90 seconds. If Harry's top speed is 1 m/sec, can he still win the race?

Use the graphing calculator to simulate the race.

Under MODE: Degree, PAR, Connected, Simul

Under WINDOW: Tmin=0; Tmax=150; Tstep=1; Xmin=0; Xmax=30; Xscl=10; Ymin= -2; Ymax=4; Yscl=1

Under Y=:
            X1T=0.2T 
Tina the Tortoise moves at a slow and steady pace.
            Y1T =1 
This places the tortoise in lane 1.
            X2T=1(t-90) 
Harry the Hare waits 90 seconds before running.
            Y2T=3 
This places the hare in lane 3.

1. (2) How far had Tina run when Harry started his sprint?

2. (2) If Harry the Hare were less boastful, he might have been able to win the race. How long could Harry actually have waited and still won? (Test your theory by running the race again with different equations for Harry.)

3. Tammy the Tortoise is even faster than her sister, Tina, so she challenges Harry to a race over an even greater distance, 30m. Tammy can run at 0.3 m/sec. Harry, realizing that he still passed Tina very quickly is again boastful and overconfident. He once more delays for 90 seconds before starting his sprint. Reset your WINDOW with Tmax=200 and Xmax=35 to extend the time and the track.

a. (2) Who wins the race ?

b. (2) How long does the race last?

c. (2) At the end of the race, how far behind is the slower contestant ?

4. Tanker A moves at 18 miles per hour and Tanker B moves at 22 miles per hour. Both are traveling from Corpus Christi to St. Petersburg, which is 900 miles directly east. Tanker A leaves at noon and Tanker B leaves at 5pm. Simulate these travels parametrically (like with the tortoise and the hare) using the graphing calculator.
 

a. (2) Write the equations you used to simulate the motion.

b. (2) Provide the WINDOW settings used to graph the equations.


c. (2) If Tanker B overtakes Tanker A, when and where does this occur?

d. (2 each) Determine the times when they each arrive at their destinations.