13 3/4 length board needed
44.4 hours
Since you need 5 lengths of 2 Âľ feet boards, multiply 2 Âľ by 5, giving
5 * 2 3/4 = 5 * 11/4 = 55/4 = 13 3/4
So the answer is 13 3/4 although technically, you'll need a board that's longer since the kerf for a saw blade is greater than 0 ( a typical saw kerf is from 1/16" to 1/8" so in reality Philly and Boston will need a board about 1/2" longer than the minimum.
For the second problem, subtract the start time from the end time for each days to figure out how many hours Allison worked each day. Then sum up the hours to get the total time Allison worked. For this problem, it's easier to convert AM/PM times to 24 hour time. Basically, keep the AM times the same and add 12 hours to the PM times. So
5:13 PM - 8:03 AM = 17:13 - 8:03 = 9:10
4:49 PM - 7:58 AM = 16:49 - 7:58 = 8:51
4:41 PM - 7:46 AM = 16:41 - 7:46 = 8:55
4:50 PM - 8:23 AM = 16:50 - 8:23 = 8:27
4:32 PM - 7:31 AM = 16:32 - 7:31 = 9:01
Now add up the hours and minutes:
9:10 + 8:51 + 8:55 + 8:27 + 9:01 = 42:144
Since you can't have 144 minutes, divide the minutes by 60 to get hours and add the whole hours to the hours and the remainder will be the minutes.
144 / 60 = 2, remainder 24
So your time worked becomes
44:24 which is 44 + 24/60 = 44.4 hours.
Since 44.4 isn't one of the available answers to pick from, I'd recommend talking to your teacher about the error in the problem.
