Whats Worse than Losing? In a Race Are you finished if you lose? When are you finished? Is there a difference between a race being finished and a person.

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