Sam can mow a lawn in 120 minutes. Melissa can mow the same lawn in 80 minutes. How long does it take for both Sam and Melissa to mow the lawn if they are working together? Express your answer as a reduced fraction.

Sam can mow a lawn every 120 minutes (work rate of 1/120), and Melissa every 80 minutes (work rate of 1/80). When they work together, their combined work rate is 1/120 + 1/80 = 1/48, which means they can mow the lawn together in 48 minutes.

Explanation:

The subject being discussed is work rate which is a fundamental concept in algebra and mathematics. In order to solve this problem, you need to calculate the combined work rate of Sam and Melissa.

First, let's express their work rates in terms of lawns mowed per minute. Sam can mow 1 lawn in 120 minutes, so his work rate is 1/120 lawns per minute. Melissa can mow 1 lawn in 80 minutes, so her work rate is 1/80 lawns per minute.

When they work together, their rates add up. So, their combined rate is 1/120 + 1/80, which equals 1/48 lawns per minute. Therefore, it would take them 48 minutes to mow one lawn together.

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