Pump-hours scaling: Three pumps working 8 hours/day empty a tank in 2 days. How many hours/day must four pumps work to empty the tank in 1 day?

Introduction / Context:Total work for the tank equals total pump-hours required. Compute the pump-hours from the first schedule, then distribute that requirement over the new number of pumps and the new duration to find the needed hours/day.

Given Data / Assumptions:

• 3 pumps * 8 hours/day * 2 days empties the tank.
• Find daily hours for 4 pumps to finish in 1 day (same pump type and rate).

Concept / Approach:Total pump-hours required = pumps * hours/day * days. This remains constant across equivalent schedules. Solve for the unknown daily hours in the second schedule by equating pump-hours.

Step-by-Step Solution:

Verification / Alternative check:Check: 4 pumps * 12 hours = 48 pump-hours, same requirement as the original schedule; hence the tank is emptied in 1 day.

Why Other Options Are Wrong:11 or 14 hours/day do not hit the constant 48 pump-hours target; 19 and 16 are also inconsistent.

Common Pitfalls:Confusing total hours with hours/day or forgetting to multiply by the number of pumps in both scenarios.

Final Answer:12