Problem: pipe p can drain the liquid from a tank in 2 / 4 the time that it takes pipe q to drain it and in 2 / 3 the time that it takes pipe r to do it . if all 3 pipes operating simultaneously but independently are used to drain liquid from the tank , then pipe q drains what portion of the liquid from the tank ?
Rationale: "suppose q can drain in 1 hr . so , rq = 1 / 1 = 1 so , rp = 1 / [ ( 2 / 4 ) rq ] = 4 / 2 also , rp = rr / ( 2 / 3 ) = > 2 = rr / ( 2 / 3 ) = > rr = 4 / 3 let h is the time it takes to drain by running all 3 pipes simultaneously so combined rate = rc = 1 / h = 1 + 2 + 4 / 3 = 13 / 3 = 1 / ( 3 / 13 ) thus running simultaneously , pipe q will drain 3 / 13 of the liquid . thus answer = a ."
annotated_formula: divide(multiply(2, 2), add(multiply(multiply(4, 2), const_2), multiply(2, 2)))