Bruce and Anne can clean their house in 4 hours working together at their respective constant rates. If Anne’s speed were doubled, they could clean their house in 3 hours working at their respective rates. How many D hours does it currently take Anne to clean the house on her own? Choose the most appropriate option:
A) 6  B) 7  C) 8  D) 12  E) 14

Rationale: "lets suppose anne and bruce take a and b hrs working separately so in 1 hour they can together finish 1 / a + 1 / b portion of the work which equals 1 / 4 ( as the work is completed in 4 hours ) after anne doubles her rate of work the portion completed by the both is 1 / a + 2 / b which is equal to 1 / 3 ( as the work is completed in d = 3 hours ) solving these 2 equations we can find b as 12 so , d"
Answer: D