Solving a Thought Problem: Growing a Field of Crops from Scratch

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Crazyevox
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just a (random) thought problem I've been trying to get my mind around... :p

lets say we wish to grow a field of crops from scratch

'x' number of new baby crops 'appear' (or begin to visibly exist) on this field per time unit (Eg. days).
hence in 't' time, we will have a total of tx baby crops.

now every baby crop grows at a constant rate of 'l' (length) units per time unit from the very moment it 'appears' on the field. each crop will continue to grow at 'l' units per time unit -until- it reaches a maximum length of 'L', after which it seizes to grow.

how do i find the total length of all crops in the field at any given time?
anyone know how i could approach this? :s
 
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So at some (discrete) time t you will have:
x baby crops
x crops of length l
x crops of length 2l
...
x crops of length L - 1

Finally you need to count the number of crops of length L, which is all the crops which have "appeared" longer than time L ago, i.e. x(t - L). You should check this statement, you might need to take t - L - 1 or t - L + 1 or something like that... just plug in some numbers.