Three pipes A, B, and C fill a tank together in 8 hours. Pipe A fills the tank twice as fast as pipe B, and pipe B fills it twice as fast as pipe C. How long will it take pipe B to fill the tank by itself?

Explanation

Let the time taken by pipe B to fill the tank alone be B hours. Given A is twice as fast as B, so A fills the tank in B/2 hours, and B is twice as fast as C, so C fills it in 2B hours. The combined rate is 1/8 tank per hour: (1/(B/2)) + (1/B) + (1/(2B)) = 1/8. Simplifying, (2/B) + (1/B) + (1/(2B)) = 1/8, which becomes (2 + 1 + 0.5)/B = 1/8, or 3.5/B = 1/8. Solving for B gives B = 28 hours.