Originally Posted by

**AlephZero** If I understand your question correctly, you just want to know how to round up to the quarter-minute. I am assume that you're writing a computer program? I can tell you how to represent the problem mathematically in terms of functions, and then perhaps someone else can provide some efficient psuedocode.

Let $\displaystyle T$ represent the time worked in minutes. We want to round $\displaystyle T$ up to the nearest quarter-minute. Thus we're only concerned with the fractional portion of $\displaystyle T,$ let's call it $\displaystyle (T)$, and let's call the integer portion $\displaystyle [T]. $ Let $\displaystyle T_r$ be the rounded time. Then

$\displaystyle T_r=\begin{cases} [T]\quad\text{if } (T)=0 \\ [T] + 0.25 \quad\text{if } 0<(T)\leq 0.25 \\ [T] +0.5\quad\text{if } 0.25<(T)\leq 0.5 \\ [T] + 0.75\quad\text{if } 0.5<(T)\leq 0.75 \\ [T] + 1\quad\text{if } 0.75<(T)<1 \end{cases}$