What's the formula for how long it takes to fill something up?

Also, can somebody point me in the right direction for the problem below? Please don't give me a solution, though.


During a rainstorm, an empty bucket moving up with vertical speed V gets filled in 2 minutes. The same bucket moving down with the same vertical speed V gets filled in 8 minutes. How long will it take to fill a motionless bucket?


I'm thinking five minutes but I'm not sure.

Guest Apr 3, 2018

Let d = bucket volume per unit area


Let u be rain velocity (positive downwards)


Bucket going up:    d = 2(u + V).           (1)

Bucket going down:  d = 8(u - V).        (2)


Bucket stationary:  d = t(u + 0).             (3)


Eliminate V from (1) and (2) to get u in terms of d, then substitute u into (3) and rearrange to get t.

Alan  Apr 3, 2018
edited by Alan  Apr 3, 2018

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