Efficiency Doubled: How Long Will it Take 8 Cooks to Bake 8 Cakes?

Efficiency is a key factor in any production process, including cooking. The question of how long it will take 8 cooks to bake 8 cakes, given that 4 cooks can bake 4 cakes in 4 hours, is a classic example of a problem involving efficiency and rate. This problem can be solved using the concept of man-hours, which is a unit of measure for the amount of work that can be done by one person in one hour. In this article, we will delve into the details of this problem and provide a comprehensive answer.

Understanding the Problem

The problem at hand is a classic example of a rate problem. In this case, we are given that 4 cooks can bake 4 cakes in 4 hours. This means that the rate of work for the cooks is 1 cake per cook per hour. The question then asks how long it will take 8 cooks to bake 8 cakes, assuming no change in rate.

Applying the Concept of Man-Hours

The concept of man-hours is crucial in solving this problem. A man-hour is a unit of measure for the amount of work that can be done by one person in one hour. In this case, we know that 4 cooks can bake 4 cakes in 4 hours. This means that the total man-hours required to bake one cake is 4 man-hours (4 cooks * 1 hour).

Solving the Problem

Now that we know the total man-hours required to bake one cake, we can calculate how long it will take 8 cooks to bake 8 cakes. Since each cake requires 4 man-hours to bake, 8 cakes will require 32 man-hours (8 cakes * 4 man-hours per cake). If we have 8 cooks working simultaneously, they can complete 8 man-hours of work in one hour. Therefore, it will take them 4 hours to complete the 32 man-hours of work required to bake 8 cakes.

Conclusion

In conclusion, it will take 8 cooks 4 hours to bake 8 cakes, assuming no change in rate. This is because the total man-hours required to bake 8 cakes is 32, and 8 cooks can complete 8 man-hours of work in one hour. This problem demonstrates the importance of understanding efficiency and rate in production processes. By understanding these concepts, we can better plan and manage our resources to achieve our production goals.