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rate of work = 1 / (deadline - current time)
What unit is the 1?
Because there are no units, the equation can only be used to compare one rate of work to another rate of work at a different time (or a different deadline).
ratio of rate of work at time t1 compared to rate of work at time t2
= rate_of_work(t1, d) / rate_of_work(t2, d)
= (1 / (d - t1)) / (1 / (d - t2))
= (d - t2) / (d - t1)
This works because the only variables left are in the same units, even if that unit itself is unspecified.
could a unit for this be s-1?
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