Eight runners who had started the course at the same time, were all running, each at a constant rate, making their way from Point A to Point B. The fraction of the distance from Point A to Point B already covered for four of the runners was: Albert: 5/8, Betty:27/40 , Cecil: 9/16 , and Dianne: 7/12. The fraction of the distance that still had to be run to get to Point B for the other four runners as: Ellie: 11/32 , Frank:1/3 ,Gail:17/48 and Harry:7/24 . Who arrived at Point B in 4th place?
To compare the progress of the eight runners, we need to find a common denominator for all the fractions provided. In this case, the least common denominator (LCD) is 480.
By multiplying Albert's fraction by 60/60, we find that Albert has covered 5/8 * 60/60 = 300/480 of the distance.
By multiplying Betty's fraction by 12/12, we find that Betty has covered 27/40 * 12/12 = 324/480 of the distance.
By multiplying Cecil's fraction by 30/30, we find that Cecil has covered 9/16 * 30/30 = 270/480 of the distance.
By multiplying Dianne's fraction by 40/40, we find that Dianne has covered 7/12 * 40/40 = 280/480 of the distance.
To find the fractions for the remaining four runners, we need to subtract their fractions from 1.
Ellie: 1 - 11/32 = 21/32. Multiplying by 15/15 gives 21/32 * 15/15 = 315/480 of the distance covered.
Frank: 1 - 1/3 = 2/3. Multiplying by 80/80 gives 2/3 * 80/80 = 160/480 of the distance covered.
Gail: 1 - 17/48 = 31/48. Multiplying by 10/10 gives 31/48 * 10/10 = 310/480 of the distance covered.
Harry: 1 - 7/24 = 17/24. Multiplying by 20/20 gives 17/24 * 20/20 = 340/480 of the distance covered.
Now we can rank the runners based on the fraction covered:
1. Betty: 324/480
2. Dianne: 280/480
3. Albert: 300/480
4. Cecil: 270/480
5. Harry: 340/480
6. Gail: 310/480
7. Ellie: 315/480
8. Frank: 160/480
Therefore, Frank arrived at Point B in 4th place.