Problem: pumps a , b , and c operate at their respective constant rates . pumps a and b , operating simultaneously , can fill a certain tank in 1 / 2 hours ; pumps a and c , operating simultaneously , can fill the tank in 1 / 2 hours ; and pumps b and c , operating simultaneously , can fill the tank in 2 hours . how many hours does it take pumps a , b , and c , operating simultaneously , to fill the tank .
Rationale: "a + b = 1 / 2 ; a + c = 1 / 2 , b + c = 2 ; add then 2 * ( a + b + c ) = 3 a + b + c = 3 / 2 hrs e"
annotated_formula: divide(subtract(add(const_3.0, 2), add(divide(2, 1), add(2, 2))), 1)