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what is the derivation behind the formula: 1/A - 1/B = 1/T

Mathematics
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What is A, B and T?
for example the question : A full bath tub will empty at an average rate of 10 mins. it will fill up to full at an aaverage rate of 8 mins if the plug is in. how long will it take to fill up to full if the plug is removed and tap is turned on?
in this question, to solve it we aply the above formula. so a = 8, b = 10 t is to be found out, answer is 40

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Other answers:

Oh yes, think about positive work done and negative work done.
I dont get it.
why is a 1/a?
i mean why do we write it like 1/a is it inverse proportionality?
The more the time it takes to get a work done, The less amount of work is done in unit time..........>>>Do u see the inverse relaationship??
Lets say I do a work in 10 minutes >>> I have done 1/10th of the work in a minute
ok so why do we have to tak unit time in this formula?
take*
is it something related to physics ? if yes please tell me the topic?
You need to get one work done. You cannot talk in terms of time.........You have to talk in terms of how much work is done Thats why...................Lets say I do the work in A minutes. U spoil the work in B minutes..............>>>>>So in unit time we do (1/A-1/B) work together. right ?? Now we know how much work we accomplish in unit time............so u can find out how much time we shall need to get the work done ;)
goo answer thanks. but why am i the one who spoils the work?? :D
good*
Just an example :P

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