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?

Rationale

At 8:45 A.M., the machine finished cutting the 50 boards.

To determine the finishing time, we first calculate the total number of cuts needed for the boards. Each board needs 2 cuts to be divided into 1-foot pieces, resulting in a total of 100 cuts for 50 boards. With each cut taking 0.3 minutes, the total cutting time is 30 minutes. Adding this to the start time of 8:15 A.M. gives us a finishing time of 8:45 A.M.

A (8:30 A.M.) YOUR ANSWER

This option suggests the machine finished cutting in just 15 minutes, which is not feasible. Since each cut takes 0.3 minutes and 100 cuts are needed, the total cutting time would exceed 15 minutes, making this choice incorrect.

B (8:45 A.M.) CORRECT

This option accurately reflects the calculated finishing time. Starting at 8:15 A.M. and accounting for the total cutting time of 30 minutes, the machine would indeed finish its task at 8:45 A.M.

C (9:15 A.M.) YOUR ANSWER

This choice indicates an additional 30 minutes beyond the actual cutting time calculated. While it is plausible that a longer operation time could occur with other factors, the problem specifies the machine operated without stopping, making this option incorrect.

D (9:55 A.M.) YOUR ANSWER

This choice suggests an excessively long duration for the cutting process, implying that the machine took 1 hour and 40 minutes to finish. This is far longer than the calculated 30 minutes required, thus making this option incorrect as well.

Conclusion

The machine's total cutting time for 50 boards, requiring 100 cuts at 0.3 minutes each, sums up to 30 minutes. Therefore, starting at 8:15 A.M. and adding 30 minutes leads to a finishing time of 8:45 A.M. This logical calculation confirms that option B is the only valid answer.

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?

At 8:45 A.M., the machine finished cutting the 50 boards.

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