Final answer:
To maximize their business outputs, Paul and either Ringo or George should wash cars, while the other person should mow lawns. By doing so, they can wash 54 cars and mow 36 lawns in total each day.
Step-by-step explanation:
The question involves Paul, Ringo, and George who have a business related to mowing lawns and washing cars. We are asked to calculate the most number of cars they can wash and lawns they can mow if two of them wash cars and one mows lawns, with each working 6 hours a day.
First, we find out how many cars each can wash or how many lawns each can mow in a day:
Paul can wash 6 cars per hour or mow 3 lawns per hour, so in 6 hours, he can wash 36 cars or mow 18 lawns.
Ringo can wash 3 cars per hour or mow 3 lawns per hour, so in 6 hours, he can wash 18 cars or mow 18 lawns.
George can wash 3 cars per hour or mow 6 lawns per hour, so in 6 hours, he can wash 18 cars or mow 36 lawns.
To maximize the total number of cars washed, we would assign the two with the highest rates of washing cars to wash cars, which are Paul and either Ringo or George. To maximize lawns mowed, we assign the one with the highest rate of mowing lawns to mow lawns, which is George.
Therefore:
Paul and Ringo/George wash cars:
Paul = 36 cars
Ringo/George = 18 cars
Total cars washed = 36 + 18 = 54 cars.
George mows lawns = 36 lawns.
Therefore, in one day, maximizing their specializations, they can wash 54 cars and mow 36 lawns in total when two of them wash cars and one mows lawns.