Whats Worse than Losing? In a Race Are you finished if you lose? When are you finished? Is there a...
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Transcript of Whats Worse than Losing? In a Race Are you finished if you lose? When are you finished? Is there a...
What’s Worse than Losing?What’s Worse than Losing?
In a RaceIn a Race
• Are you finished if you lose?
• When are you finished?
• Is there a difference between a race being finished and a person being finished?
FinishedFinished
By
Richard Holden
OverviewOverview
• The race
• The challenge
• The diameter path
• The hypotenuse path
• The winner
• The final words
Dreams of ChampionshipDreams of Championship
• Sarah (age 13)– Bicycle enthusiast– Fiercely competitive– “Win at all costs”
• Sarah’s goal– Win the grand race– Beat her friend Katie– Brag to everyone– Show off her trophy
The 100 Mile RaceThe 100 Mile Race
• Sarah’s average racing speed is 12.5 mph• Sarah’s strong point is her extremely fast start• Last year’s champion finished in 7 ½ hours• At 12.5 mph, Sarah would finish it in ____ hours8
Solution: 100 miles ÷ 12.5 mph = 8 hours
The ChallengeThe Challenge
• Somehow, Sarah would need to reduce her time by at least _____minutes to win
• She saw only two possible options:– Pedal faster (an
impossible task!!!)– Reduce the distance
she actually travels
Solution: 8 hrs – 7 ½ hrs = 30 minutes
30
Save Time by Saving MilesSave Time by Saving Miles
• Reducing her time by at least 30 min means reducing her distance by at least ____ miles
• Hint: If Sarah travels 12.5 miles in one hour, how many miles would she travel in half an hour?
Solution: 12.5 ÷ 2 = 6.25 miles
6.25
Cut Total Distance? HOW?Cut Total Distance? HOW?
• Sarah’s secret is:– She knows the area of
the race– She knows of two
shortcuts– Her initial break-away
can get her secretly to the shortcuts
– She only needs to know if the two shortcuts will save her at least 6.25 miles
The Race Track
(100 miles)
24 miles
15.7 miles
23 miles
13 miles
20 miles 4.3 miles
The First Shortcut
24 miles
15.7 miles
23 miles
13 miles
20 miles 4.3 miles
Hint: C= πD
The First Shortcut
24 miles
15.7 miles
23 miles
13 miles
20 miles 4.3 miles
C= πD2*15.7 = 3.14D31.4 = 3.14D3.14 3.14 10 = D
10 mi
Miles saved by the first shortcut? 15.7 – 10 = 5.7 miles
The Second Shortcut
24 miles
15.7 miles
23 miles
13 miles
20 miles 4.3 miles
10 mi
12 mi
5 mi ? Hint: Use the Pythagorean Theorem
The Second Shortcut
24 miles
15.7 miles
23 miles
13 miles
20 miles 4.3 miles
10 mi
12 mi
5 mi 13 miA2 + B2 = C2
52 + 122 = C2
25 + 144 = C2
169 = C2
13 = C
Miles saved by second shortcut?
11 mi
8 mi
12 + 5 – 13 = 17 – 13 = 4 mi
The Objective is Met!The Objective is Met!
• Objective was to save at least 6.25 miles– First shortcut saves
5.7 miles– Second shortcut saves
4 miles– 5.7 + 4 = 9.7 miles
saved
• The objective is met with miles to spare!!
Change of EventsChange of Events
Unfortunately---
Or perhaps fortunately---
Things did not go as planned for
Sarah
24 miles
15.7 miles
23 miles
13 miles
20 miles 4.3 miles
10 mi
12 mi
5 mi 13 mi
11 mi
8 mi
Sarah is Finished!!
Banned from all
future races
The Winner!!!The Winner!!!
Katie!• Sarah’s best friend• Finished in 7 hrs 45 min.• Followed all the rules• Was cheered by
everyone!• Received a well-earned
trophy
Sarah’s Final WordsSarah’s Final Words
“Trust me—
It’s better to finish the race, than to be finished racing.”
CreditsCredits
• Character names taken from book, The Cheat, by Amy Goldman Koss– Sarah– Katie
• Pictures and graphics from MicroSoft’s Clips Online