A tap fills a tank in $6$ hr. After half the tank is filled, three more similar taps are opened. The total…

A tap fills a tank in $6$ hr. After half the tank is filled, three more similar taps are opened. The total time taken to fill the tank is:
  1. $3$ hr $15$ min
  2. $3$ hr $30$ min
  3. $3$ hr $45$ min
  4. $4$ hr

Solution

Half the tank by $1$ tap takes $3$ hr. Then $4$ taps fill the remaining half: combined rate $= \dfrac{4}{6} = \dfrac{2}{3}$ tank/hr. Time $= \dfrac{1/2}{2/3} = \dfrac{3}{4}$ hr $= 45$ min. Total $= 3$ hr $45$ min.

Asked in: IMO

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