The problem states that a student takes 8 seconds to solve a problem, correct to the nearest second. We need to find the lower and upper limits between which this time lies, in the form $a \le t < b$, where $a$ and $b$ are constants, and $t$ represents the time.

1. Problem Description

The problem states that a student takes 8 seconds to solve a problem, correct to the nearest second. We need to find the lower and upper limits between which this time lies, in the form $a \le t < b$, where $a$ and $b$ are constants, and $t$ represents the time.

2. Solution Steps

Since the time is given to the nearest second, we can assume the time has been rounded.

If a time $t$ is rounded to the nearest second to give 8 seconds, then $t$ can be written as:

$8 - 0.5 \le t < 8 + 0.5$

$7.5 \le t < 8.5$

Here, $a = 7.5$ and $b = 8.5$.

3. Final Answer

The limits between which the time lies are $7.5 \le t < 8.5$.