12. At 8:15 A.M. one day, a machine started cutting 50 boards, each with a length of 3 feet, into 1-foot pieces. It took the machine 0.3 minute to make each cut. If the machine operated without stopping, at what time did the machine finish cutting the 50 boards?
Answer: B
The machine finished cutting the 50 boards at 8:45 A.M.
The machine required a total of 90 minutes to complete the cutting of the boards, resulting in a finish time of 8:45 A.M. when starting at 8:15 A.M.
A) 8:30 A.M.
This option is incorrect because the machine would not have completed the cuts in just 15 minutes. With 50 boards and needing to make 49 cuts, the time required exceeds this duration significantly.
B) 8:45 A.M.
This option is correct as the machine takes 0.3 minutes for each of the 49 cuts needed to produce the 1-foot pieces from the 50 boards. Thus, the total time needed is 14.7 minutes, leading to a finishing time of 8:45 A.M. when starting at 8:15 A.M.
C) 9:15 A.M.
This option is incorrect because it suggests that the cutting process took much longer than it actually did. The total cutting time of 14.7 minutes does not justify a finish time of 9:15 A.M.
D) 9:55 A.M.
This option is also incorrect because it implies a significantly longer duration for the cutting process than what is required. The machine finished well before this time given the calculated cutting duration.
Conclusion
The correct answer is 8:45 A.M. as it accurately reflects the total cutting time of 14.7 minutes required for the machine to cut 50 boards into 1-foot pieces. All other options fail to recognize the actual time needed, either suggesting completion too early or far too late.