Final answer:
Sam and Dave have individual work rates for raking the lawn of 1/4 and 1/2 lawn per hour, respectively. When working together, their combined rate is 3/4 lawn per hour, and they will complete the task in 1 hour and 20 minutes.
Step-by-step explanation:
The subject of the original question is how long it will take Sam and Dave to rake their lawn working together, knowing that Sam takes 4 hours and Dave takes 2 hours to do the job individually. First, we find the work rate for each brother, which means how much of the lawn each can rake per hour. Sam's work rate is 1 lawn per 4 hours (or 1/4 lawn per hour), and Dave's work rate is 1 lawn per 2 hours (or 1/2 lawn per hour).
Next, we add together their rates to find their combined work rate when they are working together. The sum of 1/4 and 1/2 is 3/4 lawn per hour. Now to find out how many hours it will take them to finish one whole lawn, we perform the calculation 1 divided by 3/4, which gives us 4/3 hours, or 1 hour and 20 minutes. Thus, Sam and Dave will take 1 hour and 20 minutes to rake the lawn together.