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

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

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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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