Final answer:
Hal must jump an additional 7 1/4 inches to break the high school track team's long jump record, which stands at 22 feet 9 3/4 inches, when his current best jump is 22 feet 2 1/2 inches.
Step-by-step explanation:
To calculate how much farther Hal must jump to break the high school track team's long jump record, we need to subtract Hal's best jump from the record. The current long jump record is 22 feet 9 3/4 inches, and Hal's best jump is 22 feet 2 1/2 inches.
First, we convert the inches to feet to make the subtraction easier, remembering that 1 foot = 12 inches:
Record: 22 feet + (9 + 3/4) inches
= 22 feet + 9.75 inches / 12
= 22 feet + 0.8125 feet
Hal's jump: 22 feet + (2 + 1/2) inches
= 22 feet + 2.5 inches / 12
= 22 feet + 0.2083 feet
Now we subtract Hal's jump from the record:
(22 + 0.8125) feet - (22 + 0.2083) feet = 0.8125 feet - 0.2083 feet
= 0.6042 feet
To convert back to inches: 0.6042 feet * 12 inches/foot
= 7.25 inches
Therefore, Hal must jump an additional 7 1/4 inches to break the record.