Final answer:
James took 5 minutes to complete the first lap, and the second lap took 1/12 more minutes, equaling approximately 5.4167 minutes. The third lap took 1/10 less time than the second lap, yielding roughly 4.875 minutes, which is closest to option (a) 4.6 minutes, although there seems to be a discrepancy with the provided options.
Step-by-step explanation:
The question is asking us to calculate how long it took James to complete the third lap of his training, given the times he took to finish the first and second laps and their relationships to one another.
First, we start with the time James took to run the first lap, which was 5 minutes. The second lap took him 1/12 more minutes than the first lap, so we need to calculate 5 minutes plus 1/12 of 5 minutes. 1/12 of 5 minutes is approximately 0.4167 minutes. Therefore, the time for the second lap is 5 + 0.4167 minutes, which equals approximately 5.4167 minutes.
The third lap took James 1/10 less time than the second lap. To find the time for the third lap, we subtract 1/10 of the time of the second lap from the second lap's time. 1/10 of 5.4167 is approximately 0.5417 minutes. Thus, the time for the third lap is 5.4167 - 0.5417 minutes, which equals approximately 4.875 minutes or 4 minutes and 52.5 seconds (when converted to seconds, since 0.875 minutes is 52.5 seconds).
Converting 4.875 minutes back to proper decimal minutes gives us 4.875, which is approximately 4.9 minutes, but this is not an option in the multiple choice answers. It seems there is an error here, as none of the options exactly match the calculated value. However, the closest option to our calculated time (4.9 minutes) is 4.6 minutes (Option a).