KöMaL 2009 C970

Rose, Ivy and Violet decided to solve all problems in their book of mathematics problems. Rose solves $a$ problems, Ivy solves $b$ problems and Violet solves $c$ problems a day. (Each problem is only solved by one of the girls.) If Rose solved 11 times as many problems a day, Ivy solved 7 times as many and Violet solved 9 times as many, they would finish the job in 5 days. If Rose solved 4 times as many, Ivy solved 2 times as many and Violet solved 3 times as many problems a day, they would take 16 days. How many days does it take them to get done with the solutions?