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

represent the time worked in minutes. We want to round

up to the nearest quarter-minute. Thus we're only concerned with the fractional portion of

let's call it

, and let's call the integer portion

Let

be the rounded time. Then