Answer:
To find out how much further John must jump to break the record, we need to compare his best long jump to the current record.
First, convert John's long jump to feet. His long jump is \(20 \, \text{feet} + 5 \, \frac{1}{2} \, \text{inches}\). Since there are 12 inches in a foot, convert the inches to feet:
\[20 \, \text{feet} + \frac{5}{12} \, \text{feet} = 20 \, \frac{5}{12} \, \text{feet}\]
Now, compare John's jump to the record:
\[20 \frac{5}{12} \, \text{feet} < 20 \frac{10}{4} \, \text{feet}\]
The current record is \(20 \frac{10}{4} \, \text{feet}\), and John's jump is less than that. To find how much further John must jump to break the record, subtract his best jump from the record:
\[20 \frac{10}{4} \, \text{feet} - 20 \frac{5}{12} \, \text{feet}\]
To subtract these, find a common denominator for the fractions:
\[20 \frac{10}{4} \, \text{feet} - 20 \frac{5}{12} \, \text{feet} = \frac{81}{12} \, \text{feet}\]
Now, simplify the fraction:
\[\frac{81}{12} = 6 \frac{9}{12} = 6 \frac{3}{4} \, \text{feet}\]
Therefore, John must jump \(6 \frac{3}{4}\) feet further to break the record. It's done there.
Explanation: