6 pumps, working 12 hours a day, can empty a tank in 15 days. How many hours a…

Concept

For pumps with the same efficiency, the work completed is proportional to the product of the number of pumps, working hours per day, and number of days.

Therefore, for the same tank, total pump-hours remain constant: pumps × hours per day × days = constant.

Application

1. The original work is 6 × 12 × 15 = 1080 pump-hours.

2. Let the required working time be h hours per day. Eight pumps working for 9 days provide 8 × h × 9 pump-hours.

3. Equating the work gives 8 × h × 9 = 1080, so 72h = 1080 and h = 15.

Cross-check

At 15 hours per day, 8 × 15 × 9 = 1080 pump-hours, the same as the original schedule.

Hence, the required working time is 15 hours per day.