Final answer:
It would take four cleaners three hours to clean the same room, calculated using proportional reasoning and work rates.
Step-by-step explanation:
The problem of how long it would take four people to clean the same room that three cleaners can clean in four hours relates to concepts in proportional reasoning and work rates.
With three cleaners, the total work done can be considered as 3 cleaners × 4 hours = 12 cleaner-hours. This is the amount of work needed to clean the room. When you have four cleaners working at the same rate, you can divide the total work by the number of cleaners to find the time required. 12 cleaner-hours ÷ 4 cleaners = 3 hours. Therefore, it would take four cleaners three hours to clean the same room.