Multiple choice

If Rob, Noah and Fellora work alone, then they are able to complete a piece of work in 9 days, 14 days and 18 days, respectively. If all three of them work together to complete the work and earn the income as the 15th multiple of the second-highest factor of 1,045, then what is the sum of shares of Noah and Fellora?

  1. $1,547
  2. $1,672
  3. $1,768
  4. $1,824
  5. $1,963
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Work rates: Rob=1/9, Noah=1/14, Fellora=1/18. Total rate = (14+9+7)/126 = 30/126 = 5/21. The factors of 1045 are 1, 5, 11, 19, 55, 95, 209, 1045. Second-highest factor is 209. 15th multiple is 209 * 15 = 3135. Noah and Fellora's share is proportional to their rates: (1/14 + 1/18) / (5/21) = (16/126) / (30/126) = 16/30 = 8/15. Share = 3135 * (8/15) = 1672.