Question

A high school track team's long jump record is 22 ft 6 3/4 in. This year, Arthur's best long jump is 22 ft 5 1/2 in. If long jumps are measured to the nearest quarter inch, how much farther must Arthur jump to break the record? ​

Answer 1

To compare Arthur's long jump to the record, we need to convert both measurements to the same unit. Let's convert both measurements to inches:

Record: 22 ft 6 3/4 in = (22 x 12) + 6 + 3/4 = 270 + 6 + 0.75 = 276.75 in

Arthur's jump: 22 ft 5 1/2 in = (22 x 12) + 5 + 1/2 = 270 + 5 + 0.5 = 275.5 in

To determine how much farther Arthur needs to jump to break the record, we subtract Arthur's jump distance from the record distance:

Record distance - Arthur's jump distance = 276.75 in - 275.5 in = 1.25 in

However, we are told that long jumps are measured to the nearest quarter inch. Therefore, we need to round the difference to the nearest quarter inch. Since 1.25 inches is closer to 1.25 than it is to 1.5, we round down to the nearest quarter inch. This gives us:

1.25 in ≈ 1.25/4 = 0.3125 quarters ≈ 0.25 quarters

Therefore, Arthur needs to jump an additional 0.25 quarters (or 1/16 of an inch) to break the record.