Bill can paint either two walls or one window frame in one hour. In the same time, Frank can paint either three walls or two window frames. To minimize the time spent painting, who should specialize in painting walls, and who should specialize in painting window frames?
To determine who should specialize in painting walls and who should specialize in painting window frames, we need to compare the efficiency of Bill and Frank in performing these tasks.
Let's start by calculating the rates at which Bill and Frank can complete each task.
Bill can paint either two walls or one window frame in one hour. This means that Bill takes:
- 1/2 hour to paint one wall (since he can paint two walls in one hour)
- 1 hour to paint one window frame
Frank, on the other hand, can paint either three walls or two window frames in one hour. This means that Frank takes:
- 1/3 hour to paint one wall (since he can paint three walls in one hour)
- 1/2 hour to paint one window frame
Now, let's compare the efficiencies of Bill and Frank for each task:
For painting walls:
- Bill takes 1/2 hour to paint one wall
- Frank takes 1/3 hour to paint one wall
For painting window frames:
- Bill takes 1 hour to paint one window frame
- Frank takes 1/2 hour to paint one window frame
Comparing the time taken for each task, we can conclude that:
- Bill is more efficient at painting walls since he takes less time (1/2 hour) compared to Frank (1/3 hour).
- Frank is more efficient at painting window frames since he takes less time (1/2 hour) compared to Bill (1 hour).
Therefore, to minimize the time spent painting, Bill should specialize in painting walls, and Frank should specialize in painting window frames.