Multiple choice

Pipe A can fill a tank in $4$ hours and pipe B can fill it in $6$ hours. If they are opened at alternate hours and if pipe A is opened first, in how many hours will the tank be filled?

  1. $5$ hour
  2. $5\frac{2}{3}$ hours

  3. 4 hours
  4. $4\frac{2}{3}$ hours
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A fills 1/4 per hour, B fills 1/6 per hour. In 2 hours (one cycle), they fill 1/4 + 1/6 = 5/12. In 4 hours, they fill 10/12 = 5/6. Remaining = 1/6. In the 5th hour, A fills 1/4. Since 1/6 < 1/4, it takes (1/6) / (1/4) = 2/3 hours. Total time = 4 + 2/3 = 4 2/3 hours.

AI explanation

Using the one unit work method, pipe A fills one fourth of the tank in one hour and pipe B fills one sixth of the tank in one hour. In two alternating hours they fill five twelfths of the tank, reaching ten twelfths after four hours. During the fifth hour, pipe A works alone at a rate of one fourth, leaving a remaining one twelfth of the tank. Since one fourth minus one twelfth equals one twelfth, pipe A needs another one third of an hour to finish, making the total time four and two thirds hours.

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