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?
Correct Answer: 12
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:
Pump-hours required = 3 * 8 * 2 = 48 pump-hours With 4 pumps in 1 day, hours/day = 48 / 4 = 12Verification / 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