Two pipes P and Q can fill a cistern in 10 and 15 minutes respectively. Both are opened together, but at the end of 4 minutes the first is turned off. How many more minutes will it take for the cistern to fill after the first pipe is turned off?
Choices:  A) 3.5  B) 4  C) 4.5  D) 5  E) 5.5

Rationale: "let x be the total time it takes for the cistern to fill . 4 / 10 + x / 15 = 1 x / 15 = 3 / 5 x = 9 after the first pipe is turned off , it takes 5 more minutes to fill the cistern . the answer is d ."
Answer: D