If 5 Neptunians can destroy 5 small plutos in 5 solar years, how long will 7…

Concept

For identical workers acting independently at a constant rate, total work equals number of workers × time × work rate per worker.

If both the number of workers and the amount of work are multiplied by the same factor, the required time remains unchanged.

Application

1. Five Neptunians destroy five small plutos in five solar years, so their combined rate is 5 ÷ 5 = 1 small pluto per solar year.

2. The rate of one Neptunian is 1 ÷ 5 = 1/5 small pluto per solar year.

3. The rate of seven Neptunians is 7 × 1/5 = 7/5 small plutos per solar year.

4. Time = work ÷ rate = 7 ÷ (7/5) = 5 solar years.

Cross-check

The worker count and the required number of destroyed plutos both scale from 5 to 7 by the same factor, 7/5; therefore their ratio, and hence the time, stays constant.

Result: 7 Neptunians take 5 solar years.