Question

1. analyze and persevere a high school track team’s long jump record is 21 feet $2\frac{1}{4}$ inches. pablo’s best long jump is 20 feet $9\frac{1}{2}$ inches. if long jumps are measured to the nearest quarter - inch, how much farther must pablo jump to break the record?

Explanation:

Step1: Convert feet to inches

1 foot = 12 inches, so the record is \(21\times12 + 2\frac{1}{4}=252 + 2.25 = 254.25\) inches.
Pablo's jump is \(20\times12 + 9\frac{1}{2}=240 + 9.5 = 249.5\) inches.

Step2: Find the difference

To break the record, Pablo needs to jump at least \(254.25 + 0.25 = 254.5\) inches (since it's measured to the nearest quarter - inch, to break the record he needs to exceed the record by at least a quarter - inch).
The difference is \(254.5-249.5 = 5\) inches. Convert 5 inches to feet and inches: 5 inches is 0 feet 5 inches, but let's check in terms of the original units.
Wait, another way: The record is 21 feet \(2\frac{1}{4}\) inches, Pablo's is 20 feet \(9\frac{1}{2}\) inches.
First, find the difference in feet: \(21 - 20=1\) foot.
Then the difference in inches: \(2\frac{1}{4}-9\frac{1}{2}=2.25 - 9.5=- 7.25\) inches.
So the total difference is \(1\) foot \(-7.25\) inches. Since we can't have negative inches in the difference for how much more he needs to jump, we convert 1 foot to 12 inches: \(12 - 7.25 + 0.25=5\) inches (the \(+ 0.25\) is because he needs to exceed the record by a quarter - inch to break it). So the total distance he needs to jump more is \(0\) feet \(5\) inches or \(5\) inches.

Answer:

Pablo must jump 5 inches (or 0 feet 5 inches) farther to break the record.