Problem: three pipes a , b and c can fill a tank from empty to full in 30 minutes , 20 minutes and 10 minutes respectively . when the tank is empty , all the three pipes are opened . a , b and c discharge chemical solutions p , q and r respectively . what is the proportion of solution r in the liquid in the tank after 3 minutes ?
Rationale: "part filled by ( a + b + c ) in 3 minutes = 3 ( 1 / 30 + 1 / 20 + 1 / 10 ) = 11 / 20 part filled by c in 3 minutes = 3 / 10 required ratio = 3 / 10 * 20 / 11 = 6 / 11 answer : b"
annotated_formula: multiply(divide(3, 10), divide(const_1, multiply(3, add(divide(const_1, 10), add(divide(const_1, 30), divide(const_1, 30))))))