Manny and Donaire's Lawn Mowing Efficiency: A Collaborative Approach
Manny and Donaire are brothers, and both are skilled at mowing lawns. However, their efficiency differs. Manny can mow a lawn in 2 hours, while Donaire takes 3 hours to complete the same task. This article explores how their combined efforts can speed up the process and concludes in less time.
Lawn Mowing Rates
In order to understand how Manny and Donaire can work together more efficiently, let's start by calculating their individual mowing rates.
Manny's Mowing Rate
Manny can mow a lawn in 2 hours. Therefore, the rate at which he mows is:
1 lawn ÷ 2 hours 1/2 lawn per hour
Donaire's Mowing Rate
Donaire can mow a lawn in 3 hours. Hence, his mowing rate is:
1 lawn ÷ 3 hours 1/3 lawn per hour
Combined Mowing Rate
When working together, their combined mowing rate can be calculated by adding their individual rates:
(1/2) (1/3) 5/6 lawn per hour
This means that when working together, Manny and Donaire can mow 5/6 of a lawn in one hour.
Time to Complete a Lawn Together
To determine how long it will take them to mow a full lawn together, we use the combined rate:
1 lawn ÷ (5/6) lawn per hour 6/5 hours
This translates to:
6/5 hours 1 hour and 12 minutes
Thus, working together, Manny and Donaire can mow a lawn in 1 hour and 12 minutes, significantly reducing the time compared to each working alone.
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Conclusion
By understanding and using their individual mowing rates, Manny and Donaire can significantly improve their efficiency and reduce the time required to mow a lawn. Collaborative work is not only beneficial in this scenario but can be applied to various other tasks and situations where efficiency and productivity are key.