It takes 60 turns for one vessel to empty the tank. How much turns would it take totally to empty the tank if the vessel is used alternately with another one 1/3rd its capacity?
The Usual Method
Let the vessels be A and B.
Vessel A takes 60 turns to empty the tank so vessel B will take 60 x 3 = 180 turns to empty the tank as it is only 1/3rd the size of the vessel A.
If both vessels work together of the tank will be emptied by vessel A and of it will be emptied by vessel B.
Hence, + of the tank will be emptied by one turn of each vessel A and B.
, 45 turns of vessel A and 45 turns of vessel B will empty the tank completely. Hence, total number of turns = 45 + 45 = 90.
Estimated Time to arrive at the answer = 60 seconds.
Note that capacities of vessel A to that of B = 3 : 1. Hence in one turn of each 3x + 1x = 4x tank will be emptied (where ‘x’ the constant of proportionality). The tank in turn is large.
Hence, turns of each vessel will be needed. Hence total 90 turns are needed.
Estimated Time to arrive at the answer = 15 seconds.