Final answer:
Henry can build the whole picket fence in 10.5 hours by setting up a proportion, dividing 14 hours by 4/3. None of the multiple choice answers provided is correct for this calculation.
Step-by-step explanation:
Henry can build 4/3 of a picket fence in 14 hours. To find out how long it will take him to build the whole fence, we can set up a proportion since the work done is directly proportional to the time spent. If 4/3 of the fence takes 14 hours, then one whole fence (which is 3/3 or 1) would be built in fewer hours as follows:
Total time needed (T) to build the whole fence is calculated by:
T = (14 hours) * (3/4)
T = 10.5 hours
Therefore, it would take him 10.5 hours to build the whole fence. The correct answer is not listed among the options given.