 The Quarter Horse is an American breed that excels at quick turns and stops and at sprinting short distances. Its name came from its ability to outdistance other horse breeds in short races of a quarter mile or less. Thoroughbred racing has the Kentucky Derby. Quarter Horse racing has the All American Futurity, the richest race for a two-year-old of any breed in North America.

When Quarter horse racing began, it was very expensive to lay a full mile of track so it was agreed that a straight track of a quarter of a mile, would be laid instead. It became the standard racing distance for Quarter Horses and inspired their name. Thoroughbred races are often measured in furlongs, with one furlong equal to one eighth of a mile.

1. How many furlongs are there in a quarter of a mile?

The first All American Futurity was run in 1959, with a purse of \$129,686. Today, the Futurity has an entire purse of three million dollars.

2. Write the purse value of that first All American Futurity race in expanded form.

3. How much has the purse value increased since that first race? Write your answer in word form. The total purse money is divided between the ten horses competing in the final race. The table to the left shows how much the top three finishers receive.

4. What fraction of the total purse goes to the first place finisher? Write the fraction in lowest terms.

5. How much does the second place finisher receive?

6. What percentage of the total purse goes to the third place finisher?

7. How much money goes to the fourth through tenth place finishers? Unlike the Kentucky Derby and other Thoroughbred races, the All American Futurity begins with a series of trial races.

In 2016 there were fifteen trials a day over the course of two days. The five-fastest times from the first day’s 15 trials, joined the horses with the five-fastest times from second day’s 15 trials to compete for the All American Futurity on Labor Day.

Each trial consists of not more than ten horses.

8. If there were the maximum of ten horses in each trial, how many horses competed over the course of the first two days?

The track record at Ruidoso Downs was set in the 2006 All American Futurity. No Secrets Here finished with a time of 20.886 seconds.

9. Time is kept to what place value?

The fastest American Quarter Horse in history is a horse named A Long Goodbye. He ran a time of :20.686. When he stopped the clock that day, he shaved 47/1000ths of a second off a horse named Kendall Jackson’s previous record set in 2002.

10. How much faster is A Long Goodbye’s time than No Secrets Here’s? Give your answer in word form.

11. What was Kendall Jackson’s record time set in 2002? 1. How many furlongs are there in a quarter of a mile?
One Strategy: 1/4 ÷ 1/8 = 2. There are two furlongs in a quarter of a mile.
Another strategy is to use an area model.

2. Write the purse value of that first All American Futurity race in expanded form.
Answer: \$100,000 + \$20,000 + \$9,000 + \$600 + \$80 + \$6

3. How much has the purse value increased since that first race? Write your answer in word form.
Answer: \$3,000,000 − \$129,686 = \$2,870,314. The purse value has increased by two million eight hundred seventy thousand three hundred fourteen dollars.

4. What fraction of the total purse goes to the first place finisher? Write the fraction in lowest terms.
Answer: 1,500,000 / 3,000,000 = 1/2. One half of the total purse goes to the first place finisher.

5. How much does the second place finisher receive?
Answer: \$3,000,000 × 15% = \$3,000,000 × .15 = \$450,000. The second place finisher receives \$450,000.

6. What percentage of the total purse goes to the third place finisher?
Answer: (\$255,000 ÷ \$3,000,000) × 100% = 0.085 × 100% = 8.5%. The third place finisher receives 8.5% of the total purse.

7. How much money goes to the fourth through tenth place finishers?
Step 1: \$1,500,000 (1st place money) + \$450,000 (2nd place money) + \$255,000 (3rd place money) = \$2,205,000
Step 2: \$3,000,000 − \$2,205,000 = \$795,000. The fourth through tenth place finishers share \$795,000.

8. If there were the maximum of ten horses in each trial, how many horses competed over the course of the first two days?
Step 1: 15 ( the number of trials on day one) × 10 (the maximum number of horses in each trial race) = 150 horses.
Step 2: 150 horses × 2 (number of trial days) = 300. A maximum of 300 horses started the competition.
Here again, you can reach your answer in different ways. Did you use a different strategy?

9. Time is kept to what place value?
Answer: Time is kept to the thousandths of a second.

10. How much faster is A Long Goodbye’s time than No Secrets Here’s? Give your answer in word form.
Answer: 20.886 s − 20.686 s = 0.2 s. A Long Goodbye’s time was two tenths of a second faster than No Secrets Here’s.

11. What was Kendall Jackson’s record time set in 2002?
Answer: 20.686 s + 0.047 s = 20.733 s. Kendall Jackson’s record time was 20.733 s.

Common Core:
3.NBT.A.2 – Convert between standard and expanded form
4.OA.A – Use the four operations with whole numbers to solve problems
4.NF.A.1 – Write fractions in lowest terms
4.NF.C.6 – Model decimals and fractions
5.OA.A – Write and interpret numerical expressions
5.NBT.A – Understand the place value system
5.NBT.A.3 – Read, write, and compare decimals to thousandths.
5.NBT.A.3a – Model decimals and fractions
5.NBT.B – Perform operations with multi-digit whole numbers and with decimals to hundredths
5.NF.A.1 – Write fractions in lowest terms
6.NS.B.3 – Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation

Photos:
Retama Park Horse Racing by Mark Bonica; CC BY 2.0
Ruidoso Downs; Public Domain
Retama Park Horse Racing2 by Mark Bonica; CC BY 2.0