pipes and tank question

Question

Three taps A, B and C can fill a tank in 12, 15 and 20 hours respectively. If A is open all the time and B and C are open for one hour each alternately, the tank will be full in: A. 7 hours B. 7.5 hours C. 8 hours D. 6 hours The right solution of this is 7 hours but i get 7.05 I don't know what I'm doing wrong can someone help me just in the first steps?

Answer 1

Hint: When you let the taps on for 2 hours ($A$ for $2$, $B$ and $C$ for $1$), you fill in $2/12 + 1/15 + 1/20$ of the tank. Multiplying that number by $3$ gives $<1$ and multiplying that number by $4$ gives $>1$, so the answer can be neither $C$ or $D$. The one extra hour to $A$ fills in $1/12+1/15$ of the tank and the one-and-half extra hour to $B$ fills in $1/12\cdot3/2+1/15+1/20\cdot1/2$.